Suppose that (Yi, Xi) satisfy the assumptions in Key Concept 4 3 A random sample of size n 250 is drawn and yields 5 4 3 2X, R2 0 26, SER 6 2 (3 1) (1 5) (a) Test H0 i 0 vs H1 1 0 at the 5 level (b) Construct a 95 confidence interval for 1 (c) Suppose you learned that Yi and Xi were independent Wou...

a The t statistic is with a p value of 003 since the p value is less than 0 ...

Suppose that (Yi, Xi) satisfy the assumptions in Key Concept 4.3. A random sample of size n

Question:

Suppose that (Yi, Xi) satisfy the assumptions in Key Concept 4.3. A random sample of size n = 250 is drawn and yields
Ŷ = 5.4 + 3.2X, R2 = 0.26, SER = 6.2.
(3.1) (1.5)
(a) Test H0: βi = 0 vs. H1: β1 ≠ 0 at the 5% level.
(b) Construct a 95% confidence interval for β1.
(c) Suppose you learned that Yi and Xi were independent. Would you be surprised? Explain.
(d) Suppose that Yi and Xt are independent and many samples of size n = 250 are drawn, regressions estimated, and (a) and (b) answered. In what fraction of the samples would H0 from (a) be rejected? In what fraction of samples would the value = 0 be included in the confidence interval from (b)?