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.