# 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

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.

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.

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