Chapter 10, Problem 19PT3

To determine

To identify the correct interpretation of the value of correlation coefficient:

Answer to Problem 19PT3

Option e is correct

Explanation of Solution

Given information:

Given the correlation coefficient between the first-year sales and proportion of people who have heard of the product by the end of the second month in a linear regression.

i.e. r = 0.96

From the given value of correlation coefficient, the value of coefficient of determination is obtained and which is nothing but the square of correlation coefficient r.

i.e. $r^2={0.96}^2=0.9216=92\%$

Generally, the value of coefficient of determination explains the proportion of variation in the dependent variable can be explained by the independent variable.

Therefore, the we can conclude that 92 % of the variation in first-year sales can be explained by proportion of people who have heard of the product by the end of the second month as the explanatory variable.