The dataset teengamb (available in the R library faraway) concerns a study of te

Question

The dataset teengamb (available in the R library faraway) concerns a study of teenagers gambling in Britain in 1988. In this data set, the response variable is the amount of money gambled in pounds per year, and the explanatory variables are sex (coded as male O, female 1), status (socioeconomic status score based on parents' occupation), income (in pounds per week), and verbal (verbal score in words out of 12 correctly defined) of teenagers We fit a regression model with the expenditure on gambling as the response. Below is the R output. Coeffielenta Estimate 8td. Error t valoe Pr it (Intercept) 22.55565 17.19680 1.312 0.1968 22-11833 .21111 2.694 0.0101 0.05223 0.28111 .186 0.8535 .96198 1.02539 4.839 1.79-05 2.95949 2.17215 1.362 0.103 verbal Signif. codesi0.0010.010.050.11 Residual standard cror: 22.69 on 42 degrees of Ereedon Multiple R-sqaared: 0.5267, Ad justed R-squared: 0.4816 F-statisties 11.69 on and 42 DE. p-value: 1.815e-04 (a) What percentage of variation in the response is explained by these predictors? (b) For all other predictors held constant, what would be the difference in predicted expenditure on gambling for a male compared to a (c) Write down the least squares regression equation using all the variables in the model. (d) Which variables are s

Explanation / Answer

a. as the multiple R square is .5267 hence almost 53% of the total variability is explained by regressors.

b. predicting expenditure in gambling is -22.1183.

c. ^y=22.5565-22.1183*(sex)+0.05223(status)+4.96198*(income)-2.959*(verbal)

where y^=predicted value of y

d . only status is statistically significant at 5% level .

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