The following model was fitted to a sample of 25 students using data obtained at the end of their freshman year in college. The aim was to explain students’ weight gains:
y = β0 + β1x1 + β2x2 + β3x3 + ε
where
y = weight gained, in pounds, during freshman year
x1 = average number of meals eaten per week
x2 = average number of hours of exercise per week
x3 = average number of beers consumed per week
The least squares estimates of the regression parameters were as follows:
b0 = 7.35 b1 = 0.653 b2 = -1.345 b3 = 0.613
The estimated standard errors were as follows:
sb1 = 0.189 sb2 = 0.565 sb3 = 0.243
a. Test, against the appropriate one-sided alternative, the null hypothesis that, all else being equal, hours of exercise do not linearly influence weight gain.
b. Test, against the appropriate one-sided alternative, the null hypothesis that, all else being equal, beer consumption does not linearly influence weight gain.
c. Find 90%, 95%, and 99% confidence intervals for β1.