Question

The linear correlation coefficient of a set of data points is $\left(\right),․16$.

a. Is the slope of the regression line positive or negative? Explain your answers.

b. Determine the coefficient of determination.

Short answer

a) The slope of the regression line is positive.

b) The coefficient of determination$=0.716$

Step-by-step solution

Part (a) Step 1: Given Information

To explain whether the slope of the regression line is either positive or negative.

Part (a) Step 2: Explanation

The set of data points has a correlation coefficient of $=0.846$.

The slope has the same sign as the correlation coefficient.

The coefficient of correlation is positive.

As a result, the regression line's slope is similarly positive.

Part (b) Step 1: Given Information

To find the coefficient of determination.

Part (b) Step 2: Explanation

Given information:

The correlation coefficient of a set of data points$=0.846$

Calculation:

The coefficient of determination =$(correlationcoefficient{)}^2$

$=(0.846{)}^2$

Hence, the coefficient determination$=0.716$