Question

For a data set with n independent observations, (x1,y1),....,(xn,yn) a simple linear regression is fit and the following information is obtained from the fit and ANOVA table: n=25. R^2=0.7114, b1=0.2355, F-statistic=56.68 calculate each of following. show your work. A. Correlation coefficient, rxy B. The t-statistic to test H0: ?1 = 0 vs. H1: ?1 ? 0 C. The p-value for the t-statistic calculated in part B D. The standard error of b1 E. The p-value for the F-statistic

          For a data set with n independent observations, (x1,y1),....,(xn,yn) a simple linear regression is fit and the following information is obtained from the fit and ANOVA table:

n=25. R^2=0.7114, b1=0.2355, F-statistic=56.68

calculate each of following.                         show your work.

A. Correlation coefficient, rxy
B. The t-statistic to test H0: ?1 = 0 vs. H1: ?1 ? 0
C. The p-value for the t-statistic calculated in part B
D. The standard error of b1
E. The p-value for the F-statistic

For a data set with n independent observations, (x1,y1),....,(xn,yn) a simple linear regression is fit and the following information is obtained from the fit and ANOVA table:

n=25. R^2=0.7114, b1=0.2355, F-statistic=56.68

calculate each of following. show your work.

A. Correlation coefficient, rxy
B. The t-statistic to test H0: ?1 = 0 vs. H1: ?1 ? 0
C. The p-value for the t-statistic calculated in part B
D. The standard error of b1
E. The p-value for the F-statistic

Added by Remedios W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Supreeta N

06/18/2023

Step 1

Correlation coefficient (r_xy): We know that R^2 = (r_xy)^2, so we can find r_xy by taking the square root of R^2. r_xy = ±√(0.7114) = ±0.8431 Since b1 is positive, we can assume that the correlation is positive. r_xy = 0.8431 Show more…

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For a data set with n independent observations, (X1, Y1), (X2, Y2), ..., (Xn, Yn), simple linear regression is fit and the following information is obtained from the fit and ANOVA table: n = 25, R^2 = 0.7114, b1 = 0.2355, F-statistic = 56.68. Calculate each of the following and show your work: A. Correlation coefficient; rxy B. The t-statistic to test Ho: B1 = 0, H1: B1 â‰ 0 C. The p-value for the t-statistic calculated in part B D. The standard error of b1 E. The p-value for the F-statistic