Suppose you fit the model y 0 1x1 2x2 3x3 to n 30 data points and obtain the following result y 3 4 4 6x1 2 7x2 93x3 The estimated standard errors of 2 and 3 are 1 86 and 29, respectively a Test the null hypothesis H0 2 0 against the alternative hypothesis H 2 0 Use 05 b Test the null hypothesis H0...

The regression model is y34 46x 1 27x 2 O93x 3 The sample size n 30 The standard error of 2 and 3 ar ...

Suppose you fit the model y = 0 + 1x1 + 2x2 + 3x3

Question:

Suppose you fit the model
y = β0 + β 1x1 + β 2x2 + β 3x3 + Ɛ
to n = 30 data points and obtain the following result:
ŷ = 3.4 - 4.6x1 + 2.7x2 + .93x3
The estimated standard errors of β2 and β3 are 1.86 and .29, respectively.
a. Test the null hypothesis H0: β2 = 0 against the alternative hypothesis Hα: β2 ≠ 0. Use α = .05.
b. Test the null hypothesis H0: β3 = 0 against the alternative hypothesis Hα: β2 ≠ 0. Use α = .05.
c. The null hypothesis H0: β2 = 0 is not rejected. In contrast, the null hypothesis H0: β3 = 0 is rejected. Explain how this can happen even though β2 > β3.