Question

An insurance agent has selected a sample of drivers that she insures whose ages are in the range from​ 16-42 years old. For each​ driver, she records the age of the driver and the dollar amount of claims that the driver filed in the previous 12 months. A scatterplot showing the dollar amount of claims as the response variable and the age as the predictor shows a linear trend. The least squares regression line is determined to​ be: y=3715−75.4x. A plot of the residuals versus age of the drivers showed no​ pattern, and the following were​ reported: r2=.822 Standard deviation of the residuals se=312.1 For the response variable and the predictor described​ above, is the correlation r between the variables positive or​ negative? Explain how you reached your conclusion.

A. ​Negative, because the slope is negative. B. ​Positive, because the ​y-intercept is positive. C. ​Positive, because the slope is positive. D. ​Negative, because the ​y-intercept is negative.

Answer 1

The least squares regression line is determined to​ be: y=3715−75.4x.

A plot of the residuals versus age of the drivers showed no​ pattern, and the following were​ reported: r2=.822

Standard deviation of the residuals se=312.1

Since, it is simple linear regression, correlation 'r' =

and we know, R² = 0.822, then r = = -0.9066

Correlation = -0.9066 (high and negative)

A. ​Negative, because the slope is negative.

For a unit increase in x, there is 75.4 units of decrease in Y

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