A researcher collects a sample of 20 observations of two variables x and y and calculates the following
x ̄ = 36.1
y ̄ = 100.35
sum of (xi − x ̄)2 = 4223.8
Cov (x, y) = 565.121
sum of (yi − y ̄)2 = 34366.55
Based on this data, the researcher wants to estimate the model
E[Y|X]=β0 +β1X
(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 β1?
(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.Â
Please, show some work.
