Question

Run the regression of scores on a exam (Scores) on the three variables "Hours (worked)", "Beers (consumed)" and the dummy variable for "Male". Score Hours Beers M = 1 87 7 2 0 56 2 5 1 34 1 7 1 87 6 1 0 92 11 2 0 13 2 9 1 34 0 6 1 56 4 3 0 95 10 1 0 77 7 3 0 Which of the following statements is incorrect Select one: a. All independent variables are statistically significant b. A female who consumes one beer and works one hour would expect to score about 71.23 c. A male who consumes three beers and works two hours would expect to score about 72.76 d. A male who five hours and consumes two beers would expect to score about 91.96

Answer 1

R code:

> score=scan('clipboard')
Read 10 items
> score
[1] 87 56 34 87 92 13 34 56 95 77
> hours=scan('clipboard')
Read 10 items
> hours
[1] 7 2 1 6 11 2 0 4 10 7
> beer=scan('clipboard')
Read 10 items
> beer
[1] 2 5 7 1 2 9 6 3 1 3
> gender=scan('clipboard')
Read 10 items
> gender
[1] 0 1 1 0 0 1 1 0 0 0
> fit=lm(score~hours+beer+gender)
> summary(fit)

Call:
lm(formula = score ~ hours + beer + gender)

Residuals:
Min 1Q Median 3Q Max
-5.5381 -3.1075 -0.8385 2.8424 6.2616

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 77.6695 7.9591 9.759 6.66e-05 ***
hours 3.1900 0.8773 3.636 0.010886 *
beer -9.6304 1.4793 -6.510 0.000626 ***
gender   17.5983 8.7903 2.002 0.092168 .
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 5.201 on 6 degrees of freedom
Multiple R-squared: 0.9783, Adjusted R-squared: 0.9675
F-statistic: 90.33 on 3 and 6 DF, p-value: 2.205e-05

Estimated regression equation:

Score = 77.6695 + 3.1900 hours -9.6304 beer + 17.5983 Male

At 10% level of significance all variables are statistically significant.

Statement b is incorrect. (A female who consumes one beer and works one hour would expect to score about 77.6695 ).

Statement c is correct ( A male who consumes three beers and works two hours would expect to score about 72.76)

score = 77.6695 + 3.1900 (2) -9.6304 (3) + 17.5983 = 72.76

Statement d is correct . A male who five hours and consumes two beers would expect to score about 91.96

score = 77.6695 + 3.1900 (5) -9.6304 (2) + 17.5983 = 91.96