A researcher collects a sample of 20 observations of two variables x and y and calculates the follow… Show more A researcher collects a sample of 20 observations of two variables x and y and calculates the following x Ì„ = 36.1 y Ì„ = 100.35 Î£ (xi âˆ’ x Ì„)^2 = 4223.8 Cov (x, y) = 565.121 Î£ (yi âˆ’ y Ì„))^2 = 34366.55 Based on this data, the researcher wants to estimate the model E[Y|X]=Î²0+Î²1X (a) What are the estimated coefficients b0 and b1? (b) What is R^2 for this regression? How would you interpret this value? (c) What is the predicted value of y if x = 45? (d) If the estimated standard error of b1 is sb1 = 0.305, what is the 95% confidence interval for Î²1? (e) (Optional, but highly recommended): Show that sbb = 0.305 (f) Test b1for significance at the 5% significance level (assume sbb = 0.305). Be sure to state you null and alternative hypothesis, your test statistic, and your rejection rule. Please, show some work. • Show less