Question

Use the value of the linear correlation coefficient to calculate the coefficient of determination. What does this tell you about the explained variation of the data about the regression​ line? About the unexplained​ variation?
r=0.864
a) Calculate the coefficient of determination.
​(Round to three decimal places as​ needed.)
b) What does this tell you about the explained variation of the data about the regression​ line?
c) What % of the variation can be explained by the regression line.
​(Round to one decimal place as​ needed.)
About the unexplained​ variation?
d) What % of the variation is unexplained and is due to other factors or to sampling error.
(Round to one decimal place as​ needed.)

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the Coefficient of correlation (r) = 0.864

The Coefficient of determination (R^2) :

0.864^2 = 0.747 ( 3 decimal places)

B) the Coefficient of determinationR^2 tells about the proportion of variation in the dependent variable that is predicted by the independent variable, Hence, a proportion of about 0.75 should fall within the regression line.

C) percentage variation explained :

Coefficient of determination * 100%

0.747 * 100% = 74.7%

D) unexplained variation due to other factors or sampling error :

(total variation - explained variation) = (100 - 74.7)% = 25.3%