# Question

The following model was fitted to a sample of 30 families in order to explain household milk consumption:

y = β0 + β1x1 + β2x2 + ε

where

y = milk consumption, in quarts per week

x1 = weekly income, in hundreds of dollars

x2 = family size

The least squares estimates of the regression parameters were as follows:

b0 = -0.025 b1 = 0.052 b2 = 1.14

The estimated standard errors were as follows:

sb1 = 0.023 sb2 = 0.35

a. Test, against the appropriate one-sided alternative, the null hypothesis that, for fixed family size, milk consumption does not depend linearly on income.

b. Find 90%, 95%, and 99% confidence intervals for b2.

y = β0 + β1x1 + β2x2 + ε

where

y = milk consumption, in quarts per week

x1 = weekly income, in hundreds of dollars

x2 = family size

The least squares estimates of the regression parameters were as follows:

b0 = -0.025 b1 = 0.052 b2 = 1.14

The estimated standard errors were as follows:

sb1 = 0.023 sb2 = 0.35

a. Test, against the appropriate one-sided alternative, the null hypothesis that, for fixed family size, milk consumption does not depend linearly on income.

b. Find 90%, 95%, and 99% confidence intervals for b2.

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