Business Analytics

Assignment

Q. 13 a) Develop the simple linear regression equation to predict repair time given the number of months since the last maintenance service, and use the results to test the hypothesis that no relationship exists between repair time and the number of months since the last maintenance service at the 0.05 level of significance. What is the interpretation of this relationship? What does the coefficient of determination tell you about this model?

Ans: a)

The estimated regression equation is

y^ = 2.14727 + 0.30413 * Months Since Last Service

Interpretation: For a fixed number of months since last service, we estimate that the mean repair time will increase by 0.30413 hours when the Months Since Last Service increases by 1 month.

As found from the regression analysis, the value of R2 is .534 that means that the analysis of repair time given the number of months since the last maintenance service explains 53.41% of the variability in the values of repair time can be explained by the linear relationship between the months since last service and the repair time.

This shows that this data available is not giving a very high explanation of the variability available. To define the variability in a better way, we need to add some independent variable.

b. Using the simple linear regression model developed in part a, calculate the predicted repair time and residual for each of the ten repairs in the data. Sort the data by residual (so the data are in ascending order by value of the residual). Do you see any pattern in the residuals for the two types of repair? Do you see any pattern in the residuals for the two repairpersons? Do these results suggest any potential modifications to your simple linear regression model? Now create a scatter chart with months since last service on the x-axis and repair time in hours on the y-axis for which the points representing electrical and mechanical repairs are shown in different shapes and/or colors. Create a similar scatter chart of months since last service and repair time in hours for which the points representing Bob Jones and Donna Newton repairs are shown in different shapes and/or colors, Do these charts and the results of your residual analysis suggest the same potential modifications to your simple linear regression model?