Suppose you fit the first-order multiple regression model y = 0 + 1x1 + 2x2 + 3x3

Question:

Suppose you fit the first-order multiple regression model
y = β0 + β1x1 + β2x2 + β3x3 + ε
to n = 25 data points and obtain the prediction equation
= 6.4 + 3.1x1 + .92x2
The estimated standard deviations of the sampling distributions of 1 and 2 are 2.3 and .27, respectively.
a. Test H0: β1 = 0 against Ha: β1 > 0. Use α = .05.
b. Test H0: β2 = 0 against Ha: β2 ≠ 0. Use α = .05.
c. Find a 90% confidence interval for β1. Interpret the interval.
d. Find a 99% confidence interval for β2. Interpret the interval.