Loading required package: pacman [1] "lubridate" "forcats" "stringr" "dplyr" "purrr" "readr"
[7] "tidyr" "tibble" "ggplot2" "tidyverse" "pacman" lect5
linear regression
author’s details
author’s image
setting R environment
multivariate linear regression analysis
generating dummy data
| x1 | x2 | x3 | y |
|---|---|---|---|
| -1.4189153 | 55.31654 | 24.88214 | 4798.574 |
| 2.0742629 | 40.85885 | 19.47918 | 3762.265 |
| -0.2076010 | 61.95378 | 20.18491 | 4704.574 |
| 3.2907369 | 46.19061 | 19.97652 | 4012.559 |
| 3.8724917 | 60.96752 | 19.51187 | 4740.914 |
| -4.8036025 | 51.37820 | 15.49174 | 3637.568 |
| 1.0078027 | 64.38995 | 14.97110 | 4381.711 |
| -1.6938027 | 54.58989 | 18.76212 | 4176.199 |
| 0.2391636 | 63.29888 | 11.90487 | 3992.911 |
| -0.5811786 | 50.28625 | 23.13990 | 4466.557 |
performing regression analysis
Call:
lm(formula = y ~ ., data = dd)
Coefficients:
(Intercept) x1 x2 x3
-80.64 29.91 46.52 94.93
Call:
lm(formula = y ~ ., data = dd)
Residuals:
Min 1Q Median 3Q Max
-50.469 -12.044 -2.961 16.735 30.869
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -80.639 108.157 -0.746 0.484100
x1 29.906 3.886 7.695 0.000252 ***
x2 46.521 1.375 33.833 4.44e-08 ***
x3 94.932 2.812 33.760 4.50e-08 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 29.81 on 6 degrees of freedom
Multiple R-squared: 0.9966, Adjusted R-squared: 0.9948
F-statistic: 579.5 on 3 and 6 DF, p-value: 8.888e-08generating dummy data for prediction
| x1 | x2 | x3 |
|---|---|---|
| -2.8041404 | 49.53004 | 16.28137 |
| 3.3852353 | 64.19679 | 17.93383 |
| -0.2897971 | 55.71272 | 24.16503 |
predicting output using regression model
| x1 | x2 | x3 | y |
|---|---|---|---|
| -2.8041404 | 49.53004 | 16.28137 | 3685.325 |
| 3.3852353 | 64.19679 | 17.93383 | 4709.609 |
| -0.2897971 | 55.71272 | 24.16503 | 4796.554 |
load employee data
Warning: 1 failed to parse.| id | gender | bdate | educ | jobcat | salbegin | jobtime | prevexp | minority | salary |
|---|---|---|---|---|---|---|---|---|---|
| 1 | m | 1952-02-03 | 15 | 3 | 27000 | 98 | 144 | 0 | 57000 |
| 2 | m | 1958-05-23 | 16 | 1 | 18750 | 98 | 36 | 0 | 40200 |
| 3 | f | 1929-07-26 | 12 | 1 | 12000 | 98 | 381 | 0 | 21450 |
| 4 | f | 1947-04-15 | 8 | 1 | 13200 | 98 | 190 | 0 | 21900 |
| 5 | m | 1955-02-09 | 15 | 1 | 21000 | 98 | 138 | 0 | 45000 |
| 6 | m | 1958-08-22 | 15 | 1 | 13500 | 98 | 67 | 0 | 32100 |
| id | gender | bdate | educ | jobcat | salbegin | jobtime | prevexp | minority | salary | |
|---|---|---|---|---|---|---|---|---|---|---|
| 469 | 469 | f | 1964-06-01 | 15 | 1 | 13950 | 64 | 57 | 0 | 25200 |
| 470 | 470 | m | 1964-01-22 | 12 | 1 | 15750 | 64 | 69 | 1 | 26250 |
| 471 | 471 | m | 1966-08-03 | 15 | 1 | 15750 | 64 | 32 | 1 | 26400 |
| 472 | 472 | m | 1966-02-21 | 15 | 1 | 15750 | 63 | 46 | 0 | 39150 |
| 473 | 473 | f | 1937-11-25 | 12 | 1 | 12750 | 63 | 139 | 0 | 21450 |
| 474 | 474 | f | 1968-11-05 | 12 | 1 | 14250 | 63 | 9 | 0 | 29400 |
'data.frame': 474 obs. of 10 variables:
$ id : int 1 2 3 4 5 6 7 8 9 10 ...
$ gender : chr "m" "m" "f" "f" ...
$ bdate : Date, format: "1952-02-03" "1958-05-23" ...
$ educ : int 15 16 12 8 15 15 15 12 15 12 ...
$ jobcat : int 3 1 1 1 1 1 1 1 1 1 ...
$ salbegin: int 27000 18750 12000 13200 21000 13500 18750 9750 12750 13500 ...
$ jobtime : int 98 98 98 98 98 98 98 98 98 98 ...
$ prevexp : int 144 36 381 190 138 67 114 0 115 244 ...
$ minority: int 0 0 0 0 0 0 0 0 0 0 ...
$ salary : int 57000 40200 21450 21900 45000 32100 36000 21900 27900 24000 ... id gender bdate educ
Min. : 1.0 Length:474 Min. :1929-02-10 Min. : 8.00
1st Qu.:119.2 Class :character 1st Qu.:1948-01-03 1st Qu.:12.00
Median :237.5 Mode :character Median :1962-01-23 Median :12.00
Mean :237.5 Mean :1956-10-08 Mean :13.49
3rd Qu.:355.8 3rd Qu.:1965-07-06 3rd Qu.:15.00
Max. :474.0 Max. :1971-02-10 Max. :21.00
NA's :1
jobcat salbegin jobtime prevexp
Min. :1.000 Min. : 9000 Min. :63.00 Min. : 0.00
1st Qu.:1.000 1st Qu.:12488 1st Qu.:72.00 1st Qu.: 19.25
Median :1.000 Median :15000 Median :81.00 Median : 55.00
Mean :1.411 Mean :17016 Mean :81.11 Mean : 95.86
3rd Qu.:1.000 3rd Qu.:17490 3rd Qu.:90.00 3rd Qu.:138.75
Max. :3.000 Max. :79980 Max. :98.00 Max. :476.00
minority salary
Min. :0.0000 Min. : 15750
1st Qu.:0.0000 1st Qu.: 24000
Median :0.0000 Median : 28875
Mean :0.2194 Mean : 34420
3rd Qu.:0.0000 3rd Qu.: 36938
Max. :1.0000 Max. :135000
removing data with NA
calculating age & recoding gender
| educ | jobcat | salbegin | jobtime | prevexp | minority | age | gn | salary |
|---|---|---|---|---|---|---|---|---|
| 15 | 3 | 27000 | 98 | 144 | 0 | 42 | 1 | 57000 |
| 16 | 1 | 18750 | 98 | 36 | 0 | 36 | 1 | 40200 |
| 12 | 1 | 12000 | 98 | 381 | 0 | 65 | 0 | 21450 |
| 8 | 1 | 13200 | 98 | 190 | 0 | 47 | 0 | 21900 |
| 15 | 1 | 21000 | 98 | 138 | 0 | 39 | 1 | 45000 |
| 15 | 1 | 13500 | 98 | 67 | 0 | 36 | 1 | 32100 |
'data.frame': 473 obs. of 9 variables:
$ educ : int 15 16 12 8 15 15 15 12 15 12 ...
$ jobcat : int 3 1 1 1 1 1 1 1 1 1 ...
$ salbegin: int 27000 18750 12000 13200 21000 13500 18750 9750 12750 13500 ...
$ jobtime : int 98 98 98 98 98 98 98 98 98 98 ...
$ prevexp : int 144 36 381 190 138 67 114 0 115 244 ...
$ minority: int 0 0 0 0 0 0 0 0 0 0 ...
$ age : num 42 36 65 47 39 36 38 28 48 48 ...
$ gn : num 1 1 0 0 1 1 1 0 0 0 ...
$ salary : int 57000 40200 21450 21900 45000 32100 36000 21900 27900 24000 ...linear regression for employee’s data
Call:
lm(formula = salary ~ ., data = d1)
Coefficients:
(Intercept) educ jobcat salbegin jobtime prevexp
-11771.821 455.136 5753.379 1.329 154.787 -14.582
minority age gn
-968.946 -69.214 1803.320
Call:
lm(formula = salary ~ ., data = d1)
Residuals:
Min 1Q Median 3Q Max
-23217 -3013 -738 2655 46337
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -1.177e+04 3.252e+03 -3.619 0.000328 ***
educ 4.551e+02 1.541e+02 2.954 0.003293 **
jobcat 5.753e+03 6.226e+02 9.242 < 2e-16 ***
salbegin 1.329e+00 7.037e-02 18.884 < 2e-16 ***
jobtime 1.548e+02 3.164e+01 4.893 1.38e-06 ***
prevexp -1.458e+01 5.506e+00 -2.649 0.008359 **
minority -9.689e+02 7.845e+02 -1.235 0.217386
age -6.921e+01 4.770e+01 -1.451 0.147414
gn 1.803e+03 7.744e+02 2.329 0.020311 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 6803 on 464 degrees of freedom
Multiple R-squared: 0.8443, Adjusted R-squared: 0.8416
F-statistic: 314.5 on 8 and 464 DF, p-value: < 2.2e-16data generation for prediction
| id | gender | bdate | educ | jobcat | salbegin | jobtime | prevexp | minority |
|---|---|---|---|---|---|---|---|---|
| 1 | f | 1964-07-01 | 21 | 2 | 17047 | 91 | 90 | 1 |
| 2 | f | 1962-10-16 | 10 | 2 | 57257 | 72 | 79 | 1 |
| 3 | m | 1968-05-14 | 12 | 2 | 24527 | 89 | 64 | 1 |
| 4 | f | 1938-12-27 | 18 | 2 | 11581 | 84 | 65 | 0 |
| 5 | m | 1935-03-04 | 21 | 2 | 12535 | 89 | 83 | 0 |
| 6 | f | 1946-01-29 | 8 | 1 | 18641 | 76 | 71 | 1 |
| 7 | f | 1968-04-07 | 8 | 3 | 71653 | 91 | 96 | 1 |
| 8 | m | 1963-08-08 | 15 | 1 | 51759 | 88 | 91 | 0 |
| 9 | m | 1968-03-27 | 11 | 2 | 9244 | 94 | 87 | 0 |
| 10 | f | 1955-08-07 | 10 | 1 | 45229 | 85 | 96 | 0 |
| educ | jobcat | salbegin | jobtime | prevexp | minority | age | gn |
|---|---|---|---|---|---|---|---|
| 21 | 2 | 17047 | 91 | 90 | 1 | 60 | 0 |
| 10 | 2 | 57257 | 72 | 79 | 1 | 62 | 0 |
| 12 | 2 | 24527 | 89 | 64 | 1 | 56 | 1 |
| 18 | 2 | 11581 | 84 | 65 | 0 | 85 | 0 |
| 21 | 2 | 12535 | 89 | 83 | 0 | 89 | 1 |
| 8 | 1 | 18641 | 76 | 71 | 1 | 78 | 0 |
'data.frame': 10 obs. of 8 variables:
$ educ : int 21 10 12 18 21 8 8 15 11 10
$ jobcat : int 2 2 2 2 2 1 3 1 2 1
$ salbegin: num 17047 57257 24527 11581 12535 ...
$ jobtime : num 91 72 89 84 89 76 91 88 94 85
$ prevexp : num 90 79 64 65 83 71 96 91 87 96
$ minority: num 1 1 1 0 0 1 1 0 0 0
$ age : num 60 62 56 85 89 78 56 61 56 69
$ gn : num 0 0 1 0 1 0 0 1 1 0predicting data using regression model
| educ | jobcat | salbegin | jobtime | prevexp | minority | age | gn | salarypred |
|---|---|---|---|---|---|---|---|---|
| 21 | 2 | 17047 | 91 | 90 | 1 | 60 | 0 | 39598.35 |
| 10 | 2 | 57257 | 72 | 79 | 1 | 62 | 0 | 85108.82 |
| 12 | 2 | 24527 | 89 | 64 | 1 | 56 | 1 | 47592.21 |
| 18 | 2 | 11581 | 84 | 65 | 0 | 85 | 0 | 29488.70 |
| 21 | 2 | 12535 | 89 | 83 | 0 | 89 | 1 | 34159.81 |
| 8 | 1 | 18641 | 76 | 71 | 1 | 78 | 0 | 26755.91 |
| 8 | 3 | 71653 | 91 | 96 | 1 | 56 | 0 | 112191.44 |
| 15 | 1 | 51759 | 88 | 91 | 0 | 61 | 1 | 79467.80 |
| 11 | 2 | 9244 | 94 | 87 | 0 | 56 | 1 | 28234.65 |
| 10 | 1 | 45229 | 85 | 96 | 0 | 69 | 0 | 65619.96 |