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.)

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%

the data of the detroit pistons in numerical order from least to greatest is 0.30, 0.37, 0.55, 0.62, 0.69, 0.72, 0.73, 0.75, 0.77, 0.78, 0.80, 0.81, 0.81, 0.83, 0.84, 0.89

the data of the miami heat in numerical order from least to greatest is 0.50, 0.50, 0.56, 0.57, 0.67, 0.72, 0.72, 0.72, 0.75, 0.75, 0.76, 0.81, 0.82, 0.90, 1.00, 1.00

the detroit pistons median : 1.52

the miami heat median: 1.47

the iqr of this data is 0.05