# Question

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.

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.

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