Q5. To answer this question, use Minitab whenever possible.

The owner of a caravan sales company, Mr Smith, wishes to predict gross sales. A study randomly selects 40 months and collects information about the number of sellers employed, average monthly temperatures, number of different caravan models in inventory during the month, and advertising expenditures. For this question use the data set contained in the Minitab worksheet file DataCW.MTW available through Moodle (link http://moodlecurrent.gre.ac.uk/pluginfile.php/487278/mod_ resource/content/1/DataCW.MTW)

(a) Run a correlation matrix, show your results and analyse them.

(b) Discuss the importance of each predictor variable.

(c) Which regression equation should Mr Smith use to estimate gross sales if he wishes to include all the statistically significant predictor variables? Use the 0.05 significance level.

(d) Interpret the regression coefficients in this model.

(e) What percentage of the gross sales is being explained by that model?

(f) Interpret the results of the F-test.

(g) Which regression equation would you advise Mr Smith to use? Why?

(h) How effective is the regression equation that you have chosen?

(i) Is collinearity a problem in the equation chosen in part (c), and if so, what effects might it have?

(j) 68% of the sales should fall within what distance of the sales estimated from the regression plane? Use the regression equation chosen in part (g) and justify your answer.

(k) Using the equation you selected in part (g), estimate gross sales, given the following:

• There are 4 salespeople employed

• The average temperature is 40o for the month

• There are 5 different caravan models in inventory • The advertising expenditures are £750

(l) Discuss the accuracy of this prediction.