5.7 Suppose that (Yi, Xi) satisfy the least squares assumptions in Key Concept 4.3. A random sample of size n = 250 is drawn and yields

a. Test H0 : b1 = 0 vs. H1 : b1 0 at the 5% level.

b. Construct a 95% confidence interval for b1.

c. Suppose you learned that Yi and Xi were independent. Would you be surprised? Explain.

d. Suppose that Yi and Xi 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 b1 = 0 be included in the confidence interval from (b)?

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5.4 3.2X, R2 = 0.26, SER = 6.2. (3.1) (1.5)