Discussion:
A car dealer believes there is a relationship between the number of salespeople (X) on duty and the number of cars sold (Y). The following data was collected for five different weeks at the dealership.
Number of Number of
Salespeople Cars Sold
(X) (Y)
6 79
6 64
4 49
2 23
3 52
(a)Construct a scatterplot (on the computer using Excel) between number of salespeople (x) and number of cars sold (y).Provide an assessment of the scatterplot.
(b) Calculate the coefficient of correlation by hand. Interpret the calculated correlation coefficient.
(c) Calculate the estimated intercept term (B0HAT) and slope coefficient (B1HAT) of the regression equation by hand. Express the estimated regression equation in standard form. Show all calculations by hand.
(d) Provide interpretations (as applicable to the data) for both the slope coefficient and intercept term.
(e) Calculate the Yhats, errors, SSE, MSE and Regression Standard Error (SE) by hand.
(f) Does a statistically significant (.05 alpha or one-sided p value) positive relationship exist between the number of salespeople and the number of cars sold? Hint: Conduct a formal hypothesis test on the estimated slope coefficient. Show all work. Use a .05 alpha or one-sided p to setup the decision rule for the hypothesis test.The answers to part e should be used to develop the hypothesis test.
(g) Would you use the estimated regression equation to forecast the number of cars sold?
(h) Use the estimated regression equation to predict the number of cars sold if the number of salespeople equals