Question

Johnson Filtration, Inc., provides maintenance service for water filtration 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 managers want to predict the repair time necessary for each maintenance request. Hence, repair time in hours is the dependent variable. Repair time is believed to be related to three factors; the number of months since the last 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.

Repair Time in Hours	Months Since Last Service	Type of Repair	Repairperson
2.9	2	Electrical	Donna Newton
3.0	6	Mechanical	Donna Newton
4.8	8	Electrical	Bob Jones
1.8	3	Mechanical	Donna Newton
2.9	2	Electrical	Donna Newton
4.9	7	Electrical	Bob Jones
4.2	9	Mechanical	Bob Jones
4.8	8	Mechanical	Bob Jones
4.4	4	Electrical	Bob Jones
4.5	6	Electrical	Donna Newton

A) Create a new dummy variable that is equal to 0 if the type of repair is mechanical and 1 if the type of repair is electrical. Develop the multiple regression equation in Excel to predict repair time, given the number of months since the last maintenance service and the type of repair. Let x1 represent the number of months since the last maintenance service. Let x2 represent the type of repair. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. Y-cap.JPG = _____ + ______x1 + _______x2 What are the interpretations of the estimated regression parameters? What is the coefficient of determination? B) Create a new dummy variable that is equal to 0 if the repairperson is Bob Jones and 1 if the repairperson is Donna Newton. Develop the multiple regression equation in Excel to predict repair time, given the number of months since the last maintenance service and the repairperson. Let x1 represent the number of months since the last maintenance service. Let x2 represent the repairperson. If required, round your answers to four decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Y-cap.JPG = _____ + ______x1 + _______x2 What are the interpretations of the estimated regression parameters? What is the coefficient of determination?

Answer 1

A) null hypothesis H0 : repair time is independent on the number of months since the last maintenance service and the type of repair

v/s

alternative hypothesis H1 : repair time is dependent on the number of months since the last maintenance service and the type of repair

we have created a new dummy variable

type of repair =>for mechanical = 0 and for electrical.= 1

we have to develop the multiple regression to predict repair time(y) in hours

Let the inependent variables

x1 = the number of months since the last maintenance service.

x2 = type of repair.

Y-cap =   0 + 1 x1 + 2 x2

the output on excel is,

Decision rule :-

i) if p value > 0.05 l.o.s then accept null hypothesis H0 at level of significance 0.05

ii) if p value < 0.05 l.o.s if then reject  null hypothesis H0 at level of significance 0.05

Result : here all p value < 0.05 l.o.s if then reject  null hypothesis H0 at level of significance 0.05

Interpritation : the repair time necessary for each maintenance request i.e.number of months since the last maintenance service and the type of repair

the equation is ,

Y-cap = 0.9304   + 0.3876 x1 + 1.2627 x2

The coefficient of determination R² = 0.8592

B)

null hypothesis H0 : repair time is independent on the number of months since the last maintenance service and the repairperson

v/s

alternative hypothesis H1 : repair time is dependent on the number of months since the last maintenance service and the repairperson

we have created a new dummy variable

repairperson =>for Bob Jones = 0 and for Donna Newton = 1

we have to develop the multiple regression to predict repair time(y)

Let x1 = the number of months since the last maintenance service.

Let x2 = repairperson

Y-cap =    0 +  1 x1 + 2 x2

the output on excel is,

Decision rule :-

i) if p value > 0.05 l.o.s then accept null hypothesis H0 at level of significance 0.05

ii) if p value < 0.05 l.o.s if then reject  null hypothesis H0 at level of significance 0.05

Result : here all p value > 0.05 l.o.s then accept null hypothesis H0 at level of significance 0.05

Interpritation : the repair time does not necessary for each maintenance request i.e.number of months since the last maintenance service and the repairperson

the equation is ,

Y-cap = 3.5263 + 0.1519 x1 + -1.0835 x2

The coefficient of determination R² = 0.6805

adjusted R² (0.8189) of first model > adjusted R² (0.5892) of second model

so first model is good.