Suppose that (Yi, Xi) satisfy the least squares assumptions . A random sample of size n = 250 is drawn and yields ^Y= 5.4 + 3.2X, R2 = 0.26, SER = 6.2. (3.1) (1.5)a. Test H0 : β1 = 0 vs. H1 : b1 | 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 besurprised? Explain.d. Suppose that Yi and Xi are independent and many samples of sizen = 250 are drawn, regressions estimated, and (a) and (b) answered.In what fraction of the samples would H0 from (a) be rejected? Inwhat fraction of samples would the value β1 = 0 be included in theconfidence interval from (b)?
Suppose that (Yi, Xi) satisfy the least squares assumptions . A random sample of size n = 250 is drawn and yields
^Y= 5.4 + 3.2X, R2 = 0.26, SER = 6.2.
(3.1) (1.5)
a. Test H0 : β1 = 0 vs. H1 : b1 | 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 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 β1 = 0 be included in the
confidence interval from (b)?
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