Question

A restaurant manager collected data to predict monthly sales for the restaurant from monthly advertising expenses. The model created from the data showed that 36 percent of the variation in monthly sales could be explained by monthly advertising expenses. What was the value of the correlation coefficient? *

Answer 1

Answer:

The correlation coefficient is 0.60.

Step-by-step explanation:

R-squared is a statistical quantity that measures, just how near the values are to the fitted regression line. It is also known as the coefficient-of-determination.

The coefficient of determination R² specifies the percentage of the variance in the dependent variable (Y) that is forecasted or explained by linear regression and the forecaster variable (X, also recognized as the independent-variable).

The coefficient of determination R² can be computed by the formula,

$R^{2}=[r(X,Y)]^{2}$

The coefficient of determination is the square of the correlation coefficient.

The restaurant manager wanted to estimate the monthly sales for the restaurant from monthly advertising expenses.

Here,

Y = monthly sales for the restaurant

X = monthly advertising expenses

It is provided that, 36% of the variation in monthly sales could be explained by monthly advertising expenses.

That is, the value of R² is 0.36.

Compute the correlation coefficient value between X and Y as follows:

$[r(X,Y)]^{2}=R^{2}$

               $=\sqrt{R^{2}}\\=\sqrt{0.36}\\=\pm0.60$

Now the values of monthly sales and monthly advertising expenses can never be negative.

So, the correlation between the two variables can never be negative either.

Thus, the correlation coefficient is 0.60.

Answer 2

Answer:

The value of the coefficient of correlation (r) is 0.6.

Step-by-step explanation:

It has been provided that the coefficient of determination $(R^{2} )= 0.36$.

It is known that the coefficient of determination depicts the variation in the dependent variation which is explained by the explanatory (independent) variable. The symbol used for the coefficient of determination is $(R^{2} )$.

To compute the correlation coefficient from the coefficient of determination the square root is taken.

Here, the value of the correlation coefficient can be computed as:

Correlation coefficient (r) = $\sqrt{R^{2} } = \sqrt{0.36} =0.6$

Thus, the value of the coefficient of correlation (r) is 0.6.