Question

Using the teengamb data from the faraway package in R, model gamble as the response and the other variables as predictors. Take care to investigate the possibility of interactions between sex and the other predictors.

Please use R code. Thanks!

Answer 1

>library(faraway) #loading library 'FARAWAY'
> teengamb
sex status income verbal gamble
1 1 51 2.00 8 0.00
2 1 28 2.50 8 0.00
3 1 37 2.00 6 0.00
4 1 28 7.00 4 7.30
5 1 65 2.00 8 19.60
6 1 61 3.47 6 0.10
7 1 28 5.50 7 1.45
8 1 27 6.42 5 6.60
9 1 43 2.00 6 1.70
10 1 18 6.00 7 0.10
11 1 18 3.00 6 0.10
12 1 43 4.75 6 5.40
13 1 30 2.20 4 1.20
14 1 28 2.00 6 3.60
15 1 38 3.00 6 2.40
16 1 38 1.50 8 3.40
17 1 28 9.50 8 0.10
18 1 18 10.00 5 8.40
19 1 43 4.00 8 12.00
20 0 51 3.50 9 0.00
21 0 62 3.00 8 1.00
22 0 47 2.50 9 1.20
23 0 43 3.50 5 0.10
24 0 27 10.00 4 156.00
25 0 71 6.50 7 38.50
26 0 38 1.50 7 2.10
27 0 51 5.44 4 14.50
28 0 38 1.00 6 3.00
29 0 51 0.60 7 0.60
30 0 62 5.50 8 9.60
31 0 18 12.00 2 88.00
32 0 30 7.00 7 53.20
33 0 38 15.00 7 90.00
34 0 71 2.00 10 3.00
35 0 28 1.50 1 14.10
36 0 61 4.50 8 70.00
37 0 71 2.50 7 38.50
38 0 28 8.00 6 57.20
39 0 51 10.00 6 6.00
40 0 65 1.60 6 25.00
41 0 48 2.00 9 6.90
42 0 61 15.00 9 69.70
43 0 75 3.00 8 13.30
44 0 66 3.25 9 0.60
45 0 62 4.94 6 38.00
46 0 71 1.50 7 14.40
47 0 71 2.50 9 19.20
> attach(teengamb)
> names(teengamb)
[1] "sex" "status" "income" "verbal" "gamble"
#Taking all probable interactions of sex and other predictors
> model=lm(gamble~sex+status+income+verbal+sex*status+sex*income+sex*verbal)
> summary(model)

Call:
lm(formula = gamble ~ sex + status + income + verbal + sex *
status + sex * income + sex * verbal)

Residuals:
Min 1Q Median 3Q Max
-56.654 -7.589 -1.016 3.323 83.903

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 27.6354 17.6218 1.568 0.1249   
sex -33.0132 35.0530 -0.942 0.3521   
status -0.1456 0.3316 -0.439 0.6631   
income 6.0291 1.0538 5.721 1.26e-06 ***
verbal -2.9748 2.4265 -1.226 0.2276   
sex:status 0.3529 0.5492 0.643 0.5243   
sex:income -5.3478 2.4244 -2.206 0.0334 *  
sex:verbal 2.8355 4.5973 0.617 0.5410   
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 20.98 on 39 degrees of freedom
Multiple R-squared: 0.6243, Adjusted R-squared: 0.5569
F-statistic: 9.26 on 7 and 39 DF, p-value: 1.06e-06

Among all the interactions, only sex*income interaction is significant since p-value < 0.05.
> model_final=lm(gamble~income+sex+status+verbal+sex*income) #Fitting final model
> summary(model_final)

Call:
lm(formula = gamble ~ income + sex + status + verbal + sex *
income)

Residuals:
Min 1Q Median 3Q Max
-57.109 -6.162 -0.938 2.267 86.503

Coefficients:
Estimate Std. Error t value Pr(>|t|)   
(Intercept) 19.25943 15.79635 1.219 0.22972   
income 6.19885 1.02591 6.042 3.77e-07 ***
sex 4.06362 11.51612 0.353 0.72600   
status -0.04876 0.25978 -0.188 0.85203   
verbal -2.60864 1.99386 -1.308 0.19805   
income:sex -6.43683 2.14337 -3.003 0.00454 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 20.79 on 41 degrees of freedom
Multiple R-squared: 0.6121, Adjusted R-squared: 0.5647
F-statistic: 12.94 on 5 and 41 DF, p-value: 1.417e-07

But most of the variables except income and income*sex are insignificant since p-value > 0.05 (which means failing to reject H0 : no significance of the particular variable)