Mathematics, 07.04.2020 15:59 mrsjenrucker

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? *

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Answer from: laylay1548

The value of the correlation Coefficient which measures the strength of relationship between two variables is 0.6

The proportion of variation in a variable which can be explained by the regression line is called the coefficient of determination, R² This means that, the R² value of the data is 36%R² = 36% = 0.36The Correlation Coefficient, R, which measures the strength of the relationship between the variables is the square root of R² That is ; R = √R²R = √0.36

Hence, the correlation Coefficient, R is 0.6

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Answer from: pineapplepizaaaaa

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 from: Quest

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Answer from: Quest

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