# Solving and analyzing simple regression 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 hundreds of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 20 observations, the simple linear regression model yielded the following results. (X is advertising expenditure in thousand dollars and Y is tires sold in hundreds): ∑X = 50; ∑Y = 100; ∑X2 = 225; ∑Y2 = 720; ∑XY = 390

Find the Intercept and slope and Write the Regression Equation. Also predict the amount of tires (in thousand tires) sold when money invested in advertising is $3500. Calculate the correlation coefficient and coefficient of determination. Check whether there is a relation between correlation coefficient and coefficient of determination. Calculate SSE and MSE, and standard error and t-score of the slope coefficient and comment on the significance of the slope.

SSxy = 390 - (50*100)/20 = 54 SSxx = 225 - (502)/20 = SSyy = 720- (502)/20 =

= SST.

b1= SSxy/ SSxx = 1 and b0 = b0 = - b1 = 7 - 4 = 3.

The estimated Regression Equation is:

= 3 + 1*X or simply 3 + X. Since advertising is measured in thousand dollars,

we enter 3 for 3,500 in the equation for prediction.

At X = 3, = 3 + 5 = 8 or 8 thousand tires sold.

R2 = SSR/SST = 54/____________ = ________________: the model explains ______________ variation in the tire sales.

Correlation coefficient r = SSxy/√[ SSxx SSyy] = 54/√54*____ = ______

We see that √._____ = ._______. Thus it is verified that Coefficient of Determination is the square of the Correlation coefficient

SSxy = SSxy = 390 - (50*100)/20 = 54 SSxx = 225 - (502)/20 = SSyy = 720- (502)/20 =

= SST.

b1= SSxy/ SSxx = 1 and b0 = b0 = - b1 = 7 - 4 = 3.

SSR = SS2xy/ SSxx__= ______ SSE = SST- SSR = ______________

MSE = SSE/(______) = ___________ = _______

Standard Error of Estimate = se = √____ = ____________

sb1 = se/√ SSxx = _______________________________

#### Solution Preview

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 hundreds of tires) and advertising expenditures (in thousands of dollars). Based on the data set with 20 observations, the simple linear regression model yielded the following results. (X is advertising expenditure in thousand dollars and Y is tires sold in hundreds): ∑X = 50; ∑Y = 100; ∑X2 = 225; ∑Y2 = 720; ...

#### Solution Summary

The solution gives detailed steps on solving and then analyzing one simple regression question.