The Regression()
function performs multiple aspects of a
complete regression analysis. Abbreviate with reg()
. To
illustrate, first read the Employee data included as part of
lessR. Read into the default lessR
data frame d.
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## integer: Numeric data values, integers only
## double: Numeric data values with decimal digits
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Years integer 36 1 16 7 NA 7 ... 1 2 10
## 2 Gender character 37 0 2 M M W ... W W M
## 3 Dept character 36 1 5 ADMN SALE FINC ... MKTG SALE FINC
## 4 Salary double 37 0 37 53788.26 94494.58 ... 56508.32 57562.36
## 5 JobSat character 35 2 3 med low high ... high low high
## 6 Plan integer 37 0 3 1 1 2 ... 2 2 1
## 7 Pre integer 37 0 27 82 62 90 ... 83 59 80
## 8 Post integer 37 0 22 92 74 86 ... 90 71 87
## ------------------------------------------------------------------------------------------
As an option, also read the table of variable labels. Create the
table formatted as two columns. The first column is the variable name
and the second column is the corresponding variable label. Not all
variables need to be entered into the table. The table can be a
csv
file or an Excel file.
Read the label file into the l data frame, currently the only permitted name. The labels are displayed on both the text and visualization output. Each displayed label consists of the variable name juxtaposed with the corresponding label, as shown in the display of the label file.
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 label character 8 0 8 Time of Company Employment ... Test score on legal issues after instruction
## ------------------------------------------------------------------------------------------
## label
## Years Time of Company Employment
## Gender Man or Woman
## Dept Department Employed
## Salary Annual Salary (USD)
## JobSat Satisfaction with Work Environment
## Plan 1=GoodHealth, 2=GetWell, 3=BestCare
## Pre Test score on legal issues before instruction
## Post Test score on legal issues after instruction
The brief version provides just the basic analysis, what Excel
provides, plus a scatterplot with the regression line, which becomes a
scatterplot matrix with multiple regression. Because d is the
default name of the data frame that contains the variables for analysis,
the data
parameter that names the input data frame need not
be specified. Here, specify Salary as the target or response
variable with features, or predictor variables, Years and
Pre.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ Years + Pre, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable 1: Years
## Predictor Variable 2: Pre
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 36
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 44140.971 13666.115 3.230 0.003 16337.052 71944.891
## Years 3251.408 347.529 9.356 0.000 2544.355 3958.462
## Pre -18.265 167.652 -0.109 0.914 -359.355 322.825
##
## Standard deviation of Salary: 21,822.372
##
## Standard deviation of residuals: 11,753.478 for df=33
## 95% range of residuals: 47,825.260 = 2 * (2.035 * 11,753.478)
##
## R-squared: 0.726 Adjusted R-squared: 0.710 PRESS R-squared: 0.659
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 43.827 df: 2 and 33 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Years 1 12107157290.292 12107157290.292 87.641 0.000
## Pre 1 1639658.444 1639658.444 0.012 0.914
##
## Model 2 12108796948.736 6054398474.368 43.827 0.000
## Residuals 33 4558759843.773 138144237.690
## Salary 35 16667556792.508 476215908.357
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
The full output is extensive: Summary of the analysis, estimated model, fit indices, ANOVA, correlation matrix, collinearity analysis, best subset regression, residuals and influence statistics, and prediction intervals. The motivation is to provide virtually all of the information needed for a proper regression analysis.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ Years + Pre, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable 1: Years
## Predictor Variable 2: Pre
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 36
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 44140.971 13666.115 3.230 0.003 16337.052 71944.891
## Years 3251.408 347.529 9.356 0.000 2544.355 3958.462
## Pre -18.265 167.652 -0.109 0.914 -359.355 322.825
##
## Standard deviation of Salary: 21,822.372
##
## Standard deviation of residuals: 11,753.478 for df=33
## 95% range of residuals: 47,825.260 = 2 * (2.035 * 11,753.478)
##
## R-squared: 0.726 Adjusted R-squared: 0.710 PRESS R-squared: 0.659
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 43.827 df: 2 and 33 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Years 1 12107157290.292 12107157290.292 87.641 0.000
## Pre 1 1639658.444 1639658.444 0.012 0.914
##
## Model 2 12108796948.736 6054398474.368 43.827 0.000
## Residuals 33 4558759843.773 138144237.690
## Salary 35 16667556792.508 476215908.357
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
## Salary Years Pre
## Salary 1.00 0.85 0.03
## Years 0.85 1.00 0.05
## Pre 0.03 0.05 1.00
##
## Tolerance VIF
## Years 0.998 1.002
## Pre 0.998 1.002
##
## Years Pre R2adj X's
## 1 0 0.718 1
## 1 1 0.710 2
## 0 1 -0.028 1
##
## [based on Thomas Lumley's leaps function from the leaps package]
##
##
## RESIDUALS AND INFLUENCE
##
## -- Data, Fitted, Residual, Studentized Residual, Dffits, Cook's Distance
## [sorted by Cook's Distance]
## [n_res_rows = 20, out of 36 rows of data, or do n_res_rows="all"]
## -----------------------------------------------------------------------------------------
## Years Pre Salary fitted resid rstdnt dffits cooks
## Correll, Trevon 21 97 134419.230 110648.843 23770.387 2.424 1.217 0.430
## James, Leslie 18 70 122563.380 101387.773 21175.607 1.998 0.714 0.156
## Capelle, Adam 24 83 108138.430 120658.778 -12520.348 -1.211 -0.634 0.132
## Hoang, Binh 15 96 111074.860 91158.659 19916.201 1.860 0.649 0.131
## Korhalkar, Jessica 2 74 72502.500 49292.181 23210.319 2.171 0.638 0.122
## Billing, Susan 4 91 72675.260 55484.493 17190.767 1.561 0.472 0.071
## Singh, Niral 2 59 61055.440 49566.155 11489.285 1.064 0.452 0.068
## Skrotzki, Sara 18 63 91352.330 101515.627 -10163.297 -0.937 -0.397 0.053
## Saechao, Suzanne 8 98 55545.250 68362.271 -12817.021 -1.157 -0.390 0.050
## Kralik, Laura 10 74 92681.190 75303.447 17377.743 1.535 0.287 0.026
## Anastasiou, Crystal 2 59 56508.320 49566.155 6942.165 0.636 0.270 0.025
## Langston, Matthew 5 94 49188.960 58681.106 -9492.146 -0.844 -0.268 0.024
## Afshari, Anbar 6 100 69441.930 61822.925 7619.005 0.689 0.264 0.024
## Cassinelli, Anastis 10 80 57562.360 75193.857 -17631.497 -1.554 -0.265 0.022
## Osterman, Pascal 5 69 49704.790 59137.730 -9432.940 -0.826 -0.216 0.016
## Bellingar, Samantha 10 67 66337.830 75431.301 -9093.471 -0.793 -0.198 0.013
## LaRoe, Maria 10 80 61961.290 75193.857 -13232.567 -1.148 -0.195 0.013
## Ritchie, Darnell 7 82 53788.260 65403.102 -11614.842 -1.006 -0.190 0.012
## Sheppard, Cory 14 66 95027.550 88455.199 6572.351 0.579 0.176 0.011
## Downs, Deborah 7 90 57139.900 65256.982 -8117.082 -0.706 -0.174 0.010
##
##
## PREDICTION ERROR
##
## -- Data, Predicted, Standard Error of Prediction, 95% Prediction Intervals
## [sorted by lower bound of prediction interval]
## [to see all intervals add n_pred_rows="all"]
## ----------------------------------------------
##
## Years Pre Salary pred s_pred pi.lwr pi.upr width
## Hamide, Bita 1 83 51036.850 45876.388 12290.483 20871.211 70881.564 50010.352
## Singh, Niral 2 59 61055.440 49566.155 12619.291 23892.014 75240.296 51348.281
## Anastasiou, Crystal 2 59 56508.320 49566.155 12619.291 23892.014 75240.296 51348.281
## ...
## Link, Thomas 10 83 66312.890 75139.062 11933.518 50860.137 99417.987 48557.849
## LaRoe, Maria 10 80 61961.290 75193.857 11918.048 50946.405 99441.308 48494.903
## Cassinelli, Anastis 10 80 57562.360 75193.857 11918.048 50946.405 99441.308 48494.903
## ...
## Correll, Trevon 21 97 134419.230 110648.843 12881.876 84440.470 136857.217 52416.747
## Capelle, Adam 24 83 108138.430 120658.778 12955.608 94300.394 147017.161 52716.767
##
## ----------------------------------
## Plot 1: Distribution of Residuals
## Plot 2: Residuals vs Fitted Values
## ----------------------------------
Request a briefer output with the reg_brief()
version of
the function. Standardize the predictor variables in the model by
setting the new_scale
parameter to "z"
. Plot
the residuals as a line connecting each data point to the corresponding
point on the regression line as specified with the
plot_errors
parameter. To also standardize the response
variable, set parameter scale_response
to
TRUE
.
##
## Rescaled Data, First Six Rows
## Salary Years
## Hamide, Bita 51036.85 -1.466
## Singh, Niral 61055.44 -1.291
## Korhalkar, Jessica 72502.50 -1.291
## Anastasiou, Crystal 56508.32 -1.291
## Gvakharia, Kimberly 49868.68 -1.116
## Stanley, Emma 46124.97 -1.116
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ Years, new_scale="z", plot_errors=TRUE, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable: Years
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 36
##
## Data are Standardized
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 73219.551 1930.348 37.931 0.000 69296.612 77142.490
## Years 18595.810 1957.448 9.500 0.000 14617.797 22573.823
##
## Standard deviation of Salary: 21,822.372
##
## Standard deviation of residuals: 11,582.088 for df=34
## 95% range of residuals: 47,075.271 = 2 * (2.032 * 11,582.088)
##
## R-squared: 0.726 Adjusted R-squared: 0.718 PRESS R-squared: 0.681
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 90.251 df: 1 and 34 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Model 1 12106634568.544 12106634568.544 90.251 0.000
## Residuals 34 4560922223.964 134144771.293
## Salary 35 16667556792.508 476215908.357
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
Specify a cross-validation with the kfold
parameter.
Here, specify three folds. The function automatically creates the
training and testing data sets.
##
## 3-FOLD CROSS-VALIDATION
##
## Model from Training Data Applied to Testing Data
## ---------------------------------- ----------------------------------
## fold n se MSE Rsq n sp MSE Rsq
## 1 | 24 11660.989 135978665.027 0.801 | 12 12838.368 164823701.898 -0.217
## 2 | 24 8999.503 80991061.305 0.671 | 12 19788.803 391596728.186 0.632
## 3 | 24 12329.144 152007787.595 0.734 | 12 13144.990 172790769.294 0.571
## ---------------------------------- ----------------------------------
## Mean 10996.545 122992504.642 0.735 15257.387 243070399.793 0.329
The standard output also includes \(R^2_{press}\), the value of \(R^2\) when applied to new, previously unseen data, a value comparable to the average \(R^2\) on test data.
The output of Regression()
can be stored into an R
object, here named r. The output object consists of various
components that together define the output of a comprehensive regression
analysis. R refers to the resulting output structure as a list
object.
Entering the name of the object displays the full output, the default output when the output is directed to the R console instead of saving into an R object.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ Years + Pre, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable 1: Years
## Predictor Variable 2: Pre
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 36
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 44140.971 13666.115 3.230 0.003 16337.052 71944.891
## Years 3251.408 347.529 9.356 0.000 2544.355 3958.462
## Pre -18.265 167.652 -0.109 0.914 -359.355 322.825
##
## Standard deviation of Salary: 21,822.372
##
## Standard deviation of residuals: 11,753.478 for df=33
## 95% range of residuals: 47,825.260 = 2 * (2.035 * 11,753.478)
##
## R-squared: 0.726 Adjusted R-squared: 0.710 PRESS R-squared: 0.659
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 43.827 df: 2 and 33 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Years 1 12107157290.292 12107157290.292 87.641 0.000
## Pre 1 1639658.444 1639658.444 0.012 0.914
##
## Model 2 12108796948.736 6054398474.368 43.827 0.000
## Residuals 33 4558759843.773 138144237.690
## Salary 35 16667556792.508 476215908.357
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
## Salary Years Pre
## Salary 1.00 0.85 0.03
## Years 0.85 1.00 0.05
## Pre 0.03 0.05 1.00
##
## Tolerance VIF
## Years 0.998 1.002
## Pre 0.998 1.002
##
## Years Pre R2adj X's
## 1 0 0.718 1
## 1 1 0.710 2
## 0 1 -0.028 1
##
## [based on Thomas Lumley's leaps function from the leaps package]
##
##
## RESIDUALS AND INFLUENCE
##
## -- Data, Fitted, Residual, Studentized Residual, Dffits, Cook's Distance
## [sorted by Cook's Distance]
## [n_res_rows = 20, out of 36 rows of data, or do n_res_rows="all"]
## -----------------------------------------------------------------------------------------
## Years Pre Salary fitted resid rstdnt dffits cooks
## Correll, Trevon 21 97 134419.230 110648.843 23770.387 2.424 1.217 0.430
## James, Leslie 18 70 122563.380 101387.773 21175.607 1.998 0.714 0.156
## Capelle, Adam 24 83 108138.430 120658.778 -12520.348 -1.211 -0.634 0.132
## Hoang, Binh 15 96 111074.860 91158.659 19916.201 1.860 0.649 0.131
## Korhalkar, Jessica 2 74 72502.500 49292.181 23210.319 2.171 0.638 0.122
## Billing, Susan 4 91 72675.260 55484.493 17190.767 1.561 0.472 0.071
## Singh, Niral 2 59 61055.440 49566.155 11489.285 1.064 0.452 0.068
## Skrotzki, Sara 18 63 91352.330 101515.627 -10163.297 -0.937 -0.397 0.053
## Saechao, Suzanne 8 98 55545.250 68362.271 -12817.021 -1.157 -0.390 0.050
## Kralik, Laura 10 74 92681.190 75303.447 17377.743 1.535 0.287 0.026
## Anastasiou, Crystal 2 59 56508.320 49566.155 6942.165 0.636 0.270 0.025
## Langston, Matthew 5 94 49188.960 58681.106 -9492.146 -0.844 -0.268 0.024
## Afshari, Anbar 6 100 69441.930 61822.925 7619.005 0.689 0.264 0.024
## Cassinelli, Anastis 10 80 57562.360 75193.857 -17631.497 -1.554 -0.265 0.022
## Osterman, Pascal 5 69 49704.790 59137.730 -9432.940 -0.826 -0.216 0.016
## Bellingar, Samantha 10 67 66337.830 75431.301 -9093.471 -0.793 -0.198 0.013
## LaRoe, Maria 10 80 61961.290 75193.857 -13232.567 -1.148 -0.195 0.013
## Ritchie, Darnell 7 82 53788.260 65403.102 -11614.842 -1.006 -0.190 0.012
## Sheppard, Cory 14 66 95027.550 88455.199 6572.351 0.579 0.176 0.011
## Downs, Deborah 7 90 57139.900 65256.982 -8117.082 -0.706 -0.174 0.010
##
##
## PREDICTION ERROR
##
## -- Data, Predicted, Standard Error of Prediction, 95% Prediction Intervals
## [sorted by lower bound of prediction interval]
## [to see all intervals add n_pred_rows="all"]
## ----------------------------------------------
##
## Years Pre Salary pred s_pred pi.lwr pi.upr width
## Hamide, Bita 1 83 51036.850 45876.388 12290.483 20871.211 70881.564 50010.352
## Singh, Niral 2 59 61055.440 49566.155 12619.291 23892.014 75240.296 51348.281
## Anastasiou, Crystal 2 59 56508.320 49566.155 12619.291 23892.014 75240.296 51348.281
## ...
## Link, Thomas 10 83 66312.890 75139.062 11933.518 50860.137 99417.987 48557.849
## LaRoe, Maria 10 80 61961.290 75193.857 11918.048 50946.405 99441.308 48494.903
## Cassinelli, Anastis 10 80 57562.360 75193.857 11918.048 50946.405 99441.308 48494.903
## ...
## Correll, Trevon 21 97 134419.230 110648.843 12881.876 84440.470 136857.217 52416.747
## Capelle, Adam 24 83 108138.430 120658.778 12955.608 94300.394 147017.161 52716.767
##
## ----------------------------------
## Plot 1: Distribution of Residuals
## Plot 2: Residuals vs Fitted Values
## ----------------------------------
Or, work with the components individually. Use the base R
names()
function to identify all of the output components.
Component names that begin with out_
are part of the
standard output. Other components include just data and statistics
designed to be input in additional procedures, including R markdown
documents.
## [1] "out_suggest" "call" "formula" "vars" "out_title_bck" "out_background"
## [7] "out_title_basic" "out_estimates" "out_fit" "out_anova" "out_title_mod" "out_mod"
## [13] "out_mdls" "out_title_kfold" "out_kfold" "out_title_rel" "out_cor" "out_collinear"
## [19] "out_subsets" "out_title_res" "out_residuals" "out_title_pred" "out_predict" "out_ref"
## [25] "out_Rmd" "out_Word" "out_pdf" "out_odt" "out_rtf" "out_plots"
## [31] "n.vars" "n.obs" "n.keep" "coefficients" "sterrs" "tvalues"
## [37] "pvalues" "cilb" "ciub" "anova_model" "anova_residual" "anova_total"
## [43] "se" "resid_range" "Rsq" "Rsqadj" "PRESS" "RsqPRESS"
## [49] "m_se" "m_MSE" "m_Rsq" "cor" "tolerances" "vif"
## [55] "resid.max" "pred_min_max" "residuals" "fitted" "cooks.distance" "model"
## [61] "terms"
Here, only display the estimates and their inferential analysis as part of the standard text output.
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 44140.971 13666.115 3.230 0.003 16337.052 71944.891
## Years 3251.408 347.529 9.356 0.000 2544.355 3958.462
## Pre -18.265 167.652 -0.109 0.914 -359.355 322.825
Here, display the numeric values of the coefficients.
## (Intercept) Years Pre
## 44140.97140 3251.40825 -18.26496
An analysis of hundreds or thousands of rows of data can make it
difficult to locate a specific prediction interval of interest. To
initiate a search for a specific row, first do the regression and
request all prediction intervals with parameter pred_rows
.
Then convert that output to a data frame named dp with base R
read.table()
. As a data frame, do a standard search for an
individual row for a specific prediction interval (see the Subset a Data
Frame vignette for directions to subset).
This particular conversion to a data frame requires one more step.
One or more spaces in the out_predict
output delimit
adjacent columns, but the names in this data set are formatted with a
comma followed by a space. Use base R sub()
to remove the
space after the comma before converting to a data frame.
r <- reg(Salary ~ Years, pred_rows="all", graphics=FALSE)
r$out_predict = sub(", ", ",", r$out_predict, fixed=TRUE)
dp <- read.table(text=r$out_predict)
dp[.(row.names(dp) == "Pham,Scott"),]
## Years Salary pred s_pred pi.lwr pi.upr width
## Pham,Scott 13 81871.05 84955.08 11805.96 60962.48 108947.7 47985.2
Because reg()
accomplishes its computations with base R
function lm()
, lm()
parameters can be passed
to reg()
, which then passes the values to lm()
to define the corresponding indicator variables. Here, first use base R
function contr.sum()
to calculate an effect coding contrast
matrix for a categorical variable with three levels, such as the
variable Plan in the Employee data set.
## [,1] [,2]
## 1 1 0
## 2 0 1
## 3 -1 -1
Now use the lm()
parameter contrasts
to
define the effect coding for JobSat, passed to
reg_brief()
. Contrasts only apply to factors, so convert
JobSat to an R factor before the regression analysis, a task
that should generally be done for all categorical variables in an
analysis. Here, designate the order of the levels on output displays
such as a bar graph.
d$JobSat <- factor(d$JobSat, levels=c("low", "med", "high"))
reg_brief(Salary ~ JobSat, contrasts=list(JobSat=cnt))
##
## >>> JobSat is not numeric. Converted to indicator variables.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ JobSat, contrasts=list(JobSat=cnt), Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable 1: JobSatmed
## Predictor Variable 2: JobSathigh
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 35
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 85121.843 5521.853 15.415 0.000 73874.197 96369.490
## JobSatmed -8435.630 8156.317 -1.034 0.309 -25049.505 8178.245
## JobSathigh -25664.732 8156.317 -3.147 0.004 -42278.607 -9050.857
##
## Standard deviation of Salary: 22,157.414
##
## Standard deviation of residuals: 19,909.324 for df=32
## 95% range of residuals: 81,107.933 = 2 * (2.037 * 19,909.324)
##
## R-squared: 0.240 Adjusted R-squared: 0.193 PRESS R-squared: 0.098
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 5.056 df: 2 and 32 p-value: 0.012
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## JobSatmed 1 83510016.635 83510016.635 0.211 0.649
## JobSathigh 1 3924625926.927 3924625926.927 9.901 0.004
##
## Model 2 4008135943.563 2004067971.781 5.056 0.012
## Residuals 32 12684198101.098 396381190.659
## Salary 34 16692334044.661 490951001.314
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
The \(R^2\) fit statistic compares the sum of the squared errors of the model with the X predictor variables to the sum of squared errors of the null model. The baseline of comparison, the null model, is a model with no X variables such that the fitted value for each set of X values is the mean of response variable \(y\). The corresponding slope intercept is the mean of \(y\), and the standard deviation of the residuals is the standard deviation of \(y\).
The following submits the null model for Salary, and plots the errors. Compare the variability of the residuals to a regression model of Salary with one or more predictor variables. To the extent that the inclusion of one or more predictor variables in the model reduces the variability of the data about the regression line compared to the null model, the model fits the data.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ 1, plot_errors=TRUE, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 37
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 73795.557 3583.821 20.591 0.000 66527.230 81063.883
##
## Standard deviation of Salary: 21,799.533
##
## Standard deviation of residuals: 21,799.533 for df=36
## 95% range of residuals: 88,423.006 = 2 * (2.028 * 21,799.533)
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Residuals 36 17107907732.489 475219659.236
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
Can also get the null model plot from the lessR
function Plot()
with the fit
parameter set to
"null"
.
The scatterplot is displayed as a bubble plot when both variables consist of less than 10 unique integer values. With the bubble plot, there is no overprinting of the same point so that the number of values that represent a point is displayed.
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## integer: Numeric data values, integers only
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Gender integer 351 0 2 0 0 1 ... 0 0 1
## 2 m01 integer 351 0 6 0 0 2 ... 2 1 3
## 3 m02 integer 351 0 6 4 1 1 ... 3 4 3
## 4 m03 integer 351 0 6 1 4 0 ... 3 4 3
## 5 m04 integer 351 0 6 5 4 5 ... 3 4 4
## 6 m05 integer 351 0 6 0 0 4 ... 2 3 3
## 7 m06 integer 351 0 6 5 3 4 ... 4 4 2
## 8 m07 integer 351 0 6 4 3 0 ... 4 4 2
## 9 m08 integer 351 0 6 1 0 5 ... 3 2 3
## 10 m09 integer 351 0 6 5 4 3 ... 3 3 3
## 11 m10 integer 351 0 6 4 4 4 ... 3 4 3
## 12 m11 integer 351 0 6 0 0 1 ... 1 1 2
## 13 m12 integer 351 0 6 0 1 4 ... 2 1 3
## 14 m13 integer 351 0 6 0 1 0 ... 3 1 2
## 15 m14 integer 351 0 6 0 1 0 ... 2 2 2
## 16 m15 integer 351 0 6 4 2 2 ... 3 5 3
## 17 m16 integer 351 0 6 0 4 0 ... 0 2 5
## 18 m17 integer 351 0 6 1 4 2 ... 0 2 2
## 19 m18 integer 351 0 6 3 3 4 ... 4 4 3
## 20 m19 integer 351 0 6 2 1 0 ... 0 0 1
## 21 m20 integer 351 0 6 4 0 1 ... 1 0 3
## ------------------------------------------------------------------------------------------
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(m10 ~ m02, data=dd, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: dd
##
## Response Variable: m10
## Predictor Variable: m02
##
## Number of cases (rows) of data: 351
## Number of cases retained for analysis: 351
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 4.285 0.092 46.642 0.000 4.104 4.466
## m02 -0.168 0.040 -4.184 0.000 -0.247 -0.089
##
## Standard deviation of m10: 1.138
##
## Standard deviation of residuals: 1.112 for df=349
## 95% range of residuals: 4.373 = 2 * (1.967 * 1.112)
##
## R-squared: 0.048 Adjusted R-squared: 0.045 PRESS R-squared: 0.037
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 17.502 df: 1 and 349 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Model 1 21.632 21.632 17.502 0.000
## Residuals 349 431.343 1.236
## m10 350 452.974 1.294
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
Obtain an ANCOVA by entering categorical and continuous variables as
predictor variables. For a single categorical variable and a single
continuous variable, Regression()
displays the regression
line for each level of the categorical variable.
The ANCOVA assumes that the slopes for the different levels of the categorical variable are the same for the pairing of the continuous predictor variable and continuous response variable. Visually evaluate this assumption by plotting each separate slope and scatterplot.
##
## Dept: ACCT Line: b0 = -0.8 b1 = 0.0 Fit: MSE = 12 Rsq = 0.161
##
## Dept: ADMN Line: b0 = -12.3 b1 = 0.0 Fit: MSE = 24 Rsq = 0.752
##
## Dept: FINC Line: b0 = 0.2 b1 = 0.0 Fit: MSE = 2 Rsq = 0.824
##
## Dept: MKTG Line: b0 = -14.0 b1 = 0.0 Fit: MSE = 5 Rsq = 0.916
##
## Dept: SALE Line: b0 = -4.6 b1 = 0.0 Fit: MSE = 5 Rsq = 0.813
##
Then, if the slopes are not too dissimilar, run the ANCOVA. The
categorical variable must be interpretable as a categorical variable,
either as an R variable type factor
or as a non-numerical
type character
string. If the categorical variable is coded
numerically, convert to a factor
, such as
d$CatVar <- factor(d$CatVar)
which retains the original
numerical values as the value labels.
The ANCOVA displays the appropriate Type II Sum of Squares in its ANOVA table for properly evaluating the group effect that corresponds to the entered categorical variable. Note that this SS is only displayed for an ANOVA with a single categorical variable and a single covariate
##
## >>> Dept is not numeric. Converted to indicator variables.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ Dept + Years, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable 1: DeptADMN
## Predictor Variable 2: DeptFINC
## Predictor Variable 3: DeptMKTG
## Predictor Variable 4: DeptSALE
## Predictor Variable 5: Years
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 35
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 43680.151 5634.233 7.753 0.000 32156.850 55203.452
## DeptADMN 4713.926 7302.390 0.646 0.524 -10221.137 19648.990
## DeptFINC -7822.049 8057.041 -0.971 0.340 -24300.547 8656.450
## DeptMKTG -5227.930 7275.625 -0.719 0.478 -20108.253 9652.394
## DeptSALE 762.933 6351.479 0.120 0.905 -12227.301 13753.167
## Years 3234.397 364.712 8.868 0.000 2488.478 3980.317
##
## Standard deviation of Salary: 21,881.046
##
## Standard deviation of residuals: 11,741.645 for df=29
## 95% range of residuals: 48,028.719 = 2 * (2.045 * 11,741.645)
##
## R-squared: 0.754 Adjusted R-squared: 0.712 PRESS R-squared: NA
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 17.815 df: 5 and 29 p-value: 0.000
##
## -- Analysis of Variance from Type II Sums of Squares
##
## df Sum Sq Mean Sq F-value p-value
## DeptADMN 4 534128871.049 133532217.762 0.969 0.440
## DeptFINC 1 47920138.873 47920138.873 0.348 0.560
## DeptMKTG 1 48610362.188 48610362.188 0.353 0.557
## DeptSALE 1 933561595.768 933561595.768 6.772 0.014
## Years 1 10842890397.792 10842890397.792 78.648 0.000
## Residuals 29 3998120326.431 137866218.153
##
## -- Test of Interaction
##
## Dept:Years df: 4 df resid: 25 SS: 784731402.138 F: 1.526 p-value: 0.225
##
## -- Assume parallel lines, no interaction of Dept with Years
##
## Level ACCT: y^_Salary = 43680.151 + 3234.397(x_Years)
## Level ADMN: y^_Salary = 48394.077 + 3234.397(x_Years)
## Level FINC: y^_Salary = 35858.103 + 3234.397(x_Years)
## Level MKTG: y^_Salary = 38452.221 + 3234.397(x_Years)
## Level SALE: y^_Salary = 44443.084 + 3234.397(x_Years)
##
## -- Visualize Separately Computed Regression Lines
##
## Plot(Years, Salary, by=Dept, fit="lm")
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
To do a moderation analysis, specify one of (only) two predictor
variables with the parameter mod
.
## >>> Suggestion
## # Create an R markdown file for interpretative output with Rmd = "file_name"
## reg(Salary ~ Years + Pre, mod=Pre, Rmd="eg")
##
##
## BACKGROUND
##
## Data Frame: d
##
## Response Variable: Salary
## Predictor Variable 1: Years
## Predictor Variable 2: Pre
## Predictor Variable 3: Pre.Years
##
## Number of cases (rows) of data: 37
## Number of cases retained for analysis: 36
##
##
## BASIC ANALYSIS
##
## Estimate Std Err t-value p-value Lower 95% Upper 95%
## (Intercept) 73048.486 1891.523 38.619 0.000 69195.579 76901.392
## Years 3243.027 335.204 9.675 0.000 2560.238 3925.815
## Pre 4.246 162.142 0.026 0.979 -326.026 334.517
## Pre.Years 53.181 28.517 1.865 0.071 -4.907 111.268
##
## Standard deviation of Salary: 21,822.372
##
## Standard deviation of residuals: 11,335.624 for df=32
## 95% range of residuals: 46,179.821 = 2 * (2.037 * 11,335.624)
##
## R-squared: 0.753 Adjusted R-squared: 0.730 PRESS R-squared: 0.665
##
## Null hypothesis of all 0 population slope coefficients:
## F-statistic: 32.571 df: 3 and 32 p-value: 0.000
##
## -- Analysis of Variance
##
## df Sum Sq Mean Sq F-value p-value
## Years 1 12107157290.292 12107157290.292 94.222 0.000
## Pre 1 1639658.444 1639658.444 0.013 0.911
## Pre.Years 1 446876022.168 446876022.168 3.478 0.071
##
## Model 3 12555672970.904 4185224323.635 32.571 0.000
## Residuals 32 4111883821.605 128496369.425
## Salary 35 16667556792.508 476215908.357
##
##
## MODERATION ANALYSIS
##
## Mean of Pre: 0.000
## SD of Pre: 11.864
##
## mean+1SD for Pre: b0=73098.86 b1=3873.983
## mean for Pre: b0=73048.486 b1=3243.027
## mean-1SD for Pre: b0=72998.112 b1=2612.071
##
##
## K-FOLD CROSS-VALIDATION
##
##
## RELATIONS AMONG THE VARIABLES
##
##
## RESIDUALS AND INFLUENCE
##
##
## PREDICTION ERROR
In this analysis, Pre is not a moderator of the impact of Years on Salary. There is a tendency expressed by the non-parallel lines in the visualization, and an almost significant interaction, but the interaction was not detected at the \(\alpha=0.5\) level.
For a model with a binary response variable, \(y\), specify multiple logistic regression
with the usual R formula syntax applied to the lessR
function Logit()
. The output includes the confusion matrix
and various classification fit indices.
##
## >>> Suggestions
## Recommended binary format for data files: feather
## Create with Write(d, "your_file", format="feather")
## More details about your data, Enter: details() for d, or details(name)
##
## Data Types
## ------------------------------------------------------------
## character: Non-numeric data values
## integer: Numeric data values, integers only
## double: Numeric data values with decimal digits
## ------------------------------------------------------------
##
## Variable Missing Unique
## Name Type Values Values Values First and last values
## ------------------------------------------------------------------------------------------
## 1 Gender character 340 0 2 W M W ... M W M
## 2 Weight integer 340 0 100 200 200 155 ... 185 114 180
## 3 Height integer 340 0 20 71 71 66 ... 72 63 69
## 4 Waist integer 340 0 35 43 40 31 ... 37 32 35
## 5 Hips integer 340 0 28 46 42 43 ... 38 39 44
## 6 Chest integer 340 0 27 45 42 37 ... 44 36 40
## 7 Hand double 340 0 18 8.5 9.75 8 ... 9 7.5 8.75
## 8 Shoe double 340 0 20 7.5 11 8 ... 10.5 7.5 8
## ------------------------------------------------------------------------------------------
##
## Response Variable: Gender
## Predictor Variable 1: Hand
##
## Number of cases (rows) of data: 340
## Number of cases retained for analysis: 340
##
##
## BASIC ANALYSIS
##
## -- Estimated Model of Gender for the Logit of Reference Group Membership
##
## Estimate Std Err z-value p-value Lower 95% Upper 95%
## (Intercept) -26.9237 2.7515 -9.785 0.000 -32.3166 -21.5308
## Hand 3.2023 0.3269 9.794 0.000 2.5615 3.8431
##
##
## -- Odds Ratios and Confidence Intervals
##
## Odds Ratio Lower 95% Upper 95%
## (Intercept) 0.0000 0.0000 0.0000
## Hand 24.5883 12.9547 46.6690
##
##
## -- Model Fit
##
## Null deviance: 471.340 on 339 degrees of freedom
## Residual deviance: 220.664 on 338 degrees of freedom
##
## AIC: 224.6641
##
## Number of iterations to convergence: 6
##
##
## ANALYSIS OF RESIDUALS AND INFLUENCE
## Data, Fitted, Residual, Studentized Residual, Dffits, Cook's Distance
## [sorted by Cook's Distance]
## [res_rows = 20 out of 340 cases (rows) of data]
## --------------------------------------------------------------------
## Hand Gender P(Y=1) residual rstudent dffits cooks
## 125 7.0 M 0.0109 0.9891 3.045 0.1930 0.11740
## 253 7.0 M 0.0109 0.9891 3.045 0.1930 0.11740
## 162 9.5 W 0.9706 -0.9706 -2.684 -0.2256 0.07555
## 313 9.5 W 0.9706 -0.9706 -2.684 -0.2256 0.07555
## 20 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 33 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 59 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 67 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 69 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 87 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 90 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 150 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 248 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 276 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 284 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 308 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 8 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
## 109 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
## 132 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
## 142 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
##
##
## PREDICTION
##
## Probability threshold for classification M: 0.5
##
## 0: W
## 1: M
##
## Data, Fitted Values, Standard Errors
## [sorted by fitted value]
## [pred_all=TRUE to see all intervals displayed]
## --------------------------------------------------------------------
## Hand Gender label fitted std.err
## 153 6.00 W 0 0.0004481 0.0003597
## 32 6.75 W 0 0.0049256 0.0027736
## 155 6.75 W 0 0.0049256 0.0027736
## 7 7.00 W 0 0.0109024 0.0052692
##
## ... for the rows of data where fitted is close to 0.5 ...
##
## Hand Gender label fitted std.err
## 293 8.25 M 0 0.3764 0.04188
## 311 8.25 M 0 0.3764 0.04188
## 1 8.50 W 1 0.5734 0.04274
## 9 8.50 M 1 0.5734 0.04274
## 16 8.50 M 1 0.5734 0.04274
##
## ... for the last 4 rows of sorted data ...
##
## Hand Gender label fitted std.err
## 151 11 M 1 0.9998 0.0002152
## 196 11 M 1 0.9998 0.0002152
## 257 11 M 1 0.9998 0.0002152
## 299 11 M 1 0.9998 0.0002152
## --------------------------------------------------------------------
##
##
## ----------------------------
## Specified confusion matrices
## ----------------------------
##
## Probability threshold for predicting M: 0.5
## Corresponding cutoff threshold for Hand: 8.408
##
## Baseline Predicted
## ---------------------------------------------------
## Total %Tot 0 1 %Correct
## ---------------------------------------------------
## 1 170 50.0 17 153 90.0
## Gender 0 170 50.0 147 23 86.5
## ---------------------------------------------------
## Total 340 88.2
##
## Accuracy: 88.24
## Sensitivity: 90.00
## Precision: 86.93
Specify additional probability thresholds for classification beyond
just the default 0.5 with the prob_cut
parameter.
##
## Response Variable: Gender
## Predictor Variable 1: Hand
##
## Number of cases (rows) of data: 340
## Number of cases retained for analysis: 340
##
##
## BASIC ANALYSIS
##
## -- Estimated Model of Gender for the Logit of Reference Group Membership
##
## Estimate Std Err z-value p-value Lower 95% Upper 95%
## (Intercept) -26.9237 2.7515 -9.785 0.000 -32.3166 -21.5308
## Hand 3.2023 0.3269 9.794 0.000 2.5615 3.8431
##
##
## -- Odds Ratios and Confidence Intervals
##
## Odds Ratio Lower 95% Upper 95%
## (Intercept) 0.0000 0.0000 0.0000
## Hand 24.5883 12.9547 46.6690
##
##
## -- Model Fit
##
## Null deviance: 471.340 on 339 degrees of freedom
## Residual deviance: 220.664 on 338 degrees of freedom
##
## AIC: 224.6641
##
## Number of iterations to convergence: 6
##
##
## ANALYSIS OF RESIDUALS AND INFLUENCE
## Data, Fitted, Residual, Studentized Residual, Dffits, Cook's Distance
## [sorted by Cook's Distance]
## [res_rows = 20 out of 340 cases (rows) of data]
## --------------------------------------------------------------------
## Hand Gender P(Y=1) residual rstudent dffits cooks
## 125 7.0 M 0.0109 0.9891 3.045 0.1930 0.11740
## 253 7.0 M 0.0109 0.9891 3.045 0.1930 0.11740
## 162 9.5 W 0.9706 -0.9706 -2.684 -0.2256 0.07555
## 313 9.5 W 0.9706 -0.9706 -2.684 -0.2256 0.07555
## 20 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 33 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 59 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 67 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 69 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 87 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 90 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 150 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 248 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 276 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 284 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 308 9.0 W 0.8695 -0.8695 -2.031 -0.2229 0.02611
## 8 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
## 109 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
## 132 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
## 142 8.0 M 0.2132 0.7868 1.766 0.1948 0.01462
##
##
## PREDICTION
##
## Probability threshold for classification M: 0.5
##
## 0: W
## 1: M
##
## Data, Fitted Values, Standard Errors
## [sorted by fitted value]
## [pred_all=TRUE to see all intervals displayed]
## --------------------------------------------------------------------
## Hand Gender label fitted std.err
## 153 6.00 W 0 0.0004481 0.0003597
## 32 6.75 W 0 0.0049256 0.0027736
## 155 6.75 W 0 0.0049256 0.0027736
## 7 7.00 W 0 0.0109024 0.0052692
##
## ... for the rows of data where fitted is close to 0.5 ...
##
## Hand Gender label fitted std.err
## 293 8.25 M 0 0.3764 0.04188
## 311 8.25 M 0 0.3764 0.04188
## 1 8.50 W 1 0.5734 0.04274
## 9 8.50 M 1 0.5734 0.04274
## 16 8.50 M 1 0.5734 0.04274
##
## ... for the last 4 rows of sorted data ...
##
## Hand Gender label fitted std.err
## 151 11 M 1 0.9998 0.0002152
## 196 11 M 1 0.9998 0.0002152
## 257 11 M 1 0.9998 0.0002152
## 299 11 M 1 0.9998 0.0002152
## --------------------------------------------------------------------
##
##
## ----------------------------
## Specified confusion matrices
## ----------------------------
##
## Probability threshold for predicting M: 0.3
## Corresponding cutoff threshold for Hand: 8.143
##
## Baseline Predicted
## ---------------------------------------------------
## Total %Tot 0 1 %Correct
## ---------------------------------------------------
## 1 170 50.0 17 153 90.0
## Gender 0 170 50.0 147 23 86.5
## ---------------------------------------------------
## Total 340 88.2
##
## Accuracy: 88.24
## Sensitivity: 90.00
## Precision: 86.93
##
##
##
## Probability threshold for predicting M: 0.5
## Corresponding cutoff threshold for Hand: 8.408
##
## Baseline Predicted
## ---------------------------------------------------
## Total %Tot 0 1 %Correct
## ---------------------------------------------------
## 1 170 50.0 17 153 90.0
## Gender 0 170 50.0 147 23 86.5
## ---------------------------------------------------
## Total 340 88.2
##
## Accuracy: 88.24
## Sensitivity: 90.00
## Precision: 86.93
##
##
##
## Probability threshold for predicting M: 0.7
## Corresponding cutoff threshold for Hand: 8.672
##
## Baseline Predicted
## ---------------------------------------------------
## Total %Tot 0 1 %Correct
## ---------------------------------------------------
## 1 170 50.0 39 131 77.1
## Gender 0 170 50.0 156 14 91.8
## ---------------------------------------------------
## Total 340 84.4
##
## Accuracy: 84.41
## Sensitivity: 77.06
## Precision: 90.34
Categorize Hand size into six bins. Compute the conditional mean of Gender, scored as 0 and 1, at each level of Hand size. Both variables must be numeric. The visualization approximates the form of the sigmoid function from logistic regression. The point (bubble) size depends on the sample size for the corresponding bin.
##
## Table: Summary Stats
##
## Hand Gender
## ------- ------- -------
## n 340 340
## n.miss 0 0
## min 6.000 0
## max 11.000 1
## mean 8.437 0.500
##
##
## Table: mean of Gender for levels of Hand
##
## bin n midpt mean
## --- ---------------- ---- ------- ------
## 1 [5.995,6.833] 3 6.414 0.000
## 2 (6.833,7.667] 81 7.250 0.025
## 3 (7.667,8.500] 111 8.083 0.333
## 4 (8.500,9.333] 84 8.917 0.857
## 5 (9.333,10.167] 51 9.750 0.961
## 6 (10.167,11.005] 10 10.586 1.000
The parameter Rmd
creates an R markdown file that is
automatically generated and then the corresponding html document from
knitting the various output components together with full
interpretation. A new, much more complete form of computer output.
Not run here.
reg(Salary ~ Years + Pre, Rmd="eg")
Use the base R help()
function to view the full manual
for Regression()
. Simply enter a question mark followed by
the name of the function, or its abbreviation.
?reg