A researcher collects a sample of 20 observations of two variables x and y and c

Question

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

Σ (xi − x ̄)^2 = 4223.8

Cov (x, y) = 565.121

Σ (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.

Please, show some work.

Explanation / Answer

www.ssric.org/files/census/pdf/Chapt_4_Association.pdf

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