Question

A local tire dealer wants to predict the number of tires sold each month. He believes that the number of tires sold is a linear function of the amount of money invested in advertising. He randomly selects 6 months of data consisting of tire sales (in thousands of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 6 observations, the simple linear regression model yielded the following results. ?X =24 ?X2=124 ?Y = 42 ?Y2 =338 ?XY =196 Calculate the coefficient of determination and the coefficient of correlation between X and Y. Interpret the coefficient of Determination. also find the slope and intercept and write the estimated Regression equation. What would the predicted sales of tires be if he spends five thousand dollars in advertising?

Computer typing only please.

Answer 1

The coefficient of correlation between X and Y is calculated using the following equation

Coefficient of correlation between X & Y (r) = 0.7977

Coefficient of determination is calculated by squaring the correlation coefficient.

Coefficient of determination r² = 0.6363

The coefficient of determination is calculated as 0.6363 which signifies that 63.63 % of the variation in y can be accounted for by the variance in x - which is a significant coefficient of determination.

--------------------------------------------------------------------------------------

The regression equation is given as

y = a + bx

where a = intercept

b = slope

The value of aand bare calculated as follows:-

b = 1

a = 3

The regression equation is given as

y = 3 + x

The predicted sales of tires be if he spends five thousand dollars in advertising

y = 3 + 1 × 5000

Predicted sales of tires = 5003 units (If he spends five thousand dollars in advertising )