Q. 4.132 - Elementary Statistics

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.

Step-by-Step Solution

Answer

a) The slope of the regression line is positive.

b) The coefficient of determination $=0.716$

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 $=0.716$