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
The regression sum of squares and error sum of squares were found to be as follows:
SSR = 79.2 and SSE = 45.9
a. Test the null hypothesis:
H0: β1 = β2 = β3 = 0
b. Set out the analysis of variance table.