Question

The correlation coefficient r between the age of a homeowner, x, and the number of years remaining on the homeowner's mortgage, y, is 0.485.
What percent of the variation in the number of years remaining on a mortgage can be explained by differences in homeowners' ages?

Question 9 options:

23.5%


48.5%


51.5%


97%

Answer 1

Solution: We are given that the correlation coefficient between the age of a homeowner, x , and the number of years remaining on the homeowner's mortgage, y, is 0.485

We know that coefficient of determination is the percent of the variation in the dependent variable that is explained by the independent variable. The coefficient of determination is the square of correlation coefficient and is denoted by $R^{2}$

Therefore, we have:

$R^{2}= 0.485^{2}=0.235 or 23.5\%$ denotes

Hence the option 23.5% is correct