Question

Johnson Filtration, Inc., provides maintenance service for water fitration systems throughout southern Florida. Customers contact Johnson with requests for maintenance service on their water filtration systems. To estimate the service time and the service cost Johnson's manacers want to predict the repair time necessary or each maintenance request. Hence, repair time in hours is the dependent variable. Repair tme is believed to be related to three factors; the number of months snce the as maintenance service, the type of repair problem (mechanical or electrical), and the repairperson who performs the repair (Donna Newton or Bob Jones). Data for a sample of 10 service calls are reported in the following table Click on the datafile logo to reference the data r Time in Months Since Last Service Type of Repair Repairperson 2.9 Donna Donna Bob Jones Donna N Donna Bob Jones 4.8 1.8 2.9 4.9 4.2 4,8 4.4 4.5 Mechanical Mechanica Bob Jones Mechanica Bob Jones Bob Jones (a) Use the data to develop the simple linear regression equation to predict repair time given the number of months since the last maintenance service. Let x represent the number of months since the last maintenance service. If required, round your answers to four decrnal places. For subtractive or negative numbers use 교 minus sign even if there is a + sign before the blank. (Example:-300). 2.1470.304ex 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? The input in the box below will not be graded, but may be reviewed and considered by your instructor What is the coefficient of determination? If required, round your answers to four decimal places Interpret the coefficient of determination. The input in the box below will not be graded, but may be reviewed and considered by your instructor, (b) Using the simple linear regression model developed in part (a), calculate the predicted repair time and residual for each of the 10 repairs in the data. If required, round your answers to four decimal places Predicted Repair Time in Hours r Time Months Since in Hours 1.8 3.0 4.2 2.9 Last Service Type of Repair Repairperson Donna Newton Mechanica Donna Newton Residuals Mechanica Bob Jones Donna Newton

Answer 1

(a) $\hat{y}$ = 2.1473 + (0.3041) $x$.
We carry out a test of hypothesis to check whether the regression coefficient of "x" is 0 (insignificant and no linear relationship) or not. The p-value for this test has come out to be 0.016 which is less than 0.05 (level of significance). This tells us that the regression coefficient is significant and, hence, there indeed exists a linear relationship between repair time and number of months since last service.

Coefficient of determination = 0.5342.
The value of the coefficient is 0.5342 or 53.42% which tells us that the 53.42% of the variation in the repair time (dependent) variable can be explained due to this linear regression between repair time and number of months since last service. Such value also tells us that this linear fit is a moderate one, that is, it is neither too good or too bad.

(b) The table is given below:

Predicted Repair	Residuals
3.0597	-1.2597
3.9721	-0.9721
4.8845	-0.6845
2.7555	0.1445