The following output summarizes the results of fitting a least squares regression to simulated data. Because we constructed these data using a computer, we know the SRM holds and we know the parameters of the model. We chose β0 = 7, β1 = 0.5, and σe = 1.5. The ft is to a sample of n = 50 cases.

(a) If β1 = 1 / 2 in the population, then why isn€™t β1 = 1 / 2?
(b) Do the 95% confidence intervals for β0 and β1 €œwork€ in this example? (By €œwork,€ we mean that these intervals contain β0 and β1, respectively.)
(c) What€™s going to change in this summary if we increase the sample size from n = 50 to n = 5,000?

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15 12.5 10 7.5 2 2.5 -10 5 5 0 2 0.860112 s 1.28311 50 Estimate Std Error Intercept 6.993459 0.181933 bi 0.5134397 0.029887 Term