Question

Refer to the Johnson Filtration problem introduced in this section. Suppose that in addition to information on the number of months since the machine was serviced and whether a mechanical or an electrical repair was necessary, the managers obtained a list showing which repairperson performed the service. The revised data follow.

Repair Time in Hours	Months Since Last Service	Type of Repair	Repairperson
2.9	2	Electrical	Dave Newton
3.0	6	Mechanical	Dave Newton
4.8	8	Electrical	Bob Jones
1.8	3	Mechanical	Dave Newton
2.9	2	Electrical	Dave 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	Dave Newton

1. At the .05 level, are there significant relationship between the dependent variable and the independent variables?
2. What is the multiple coefficient of determination?
3. What is the adjusted multiple coefficient of determination?
4. Interpret the results.

Answer 1

Here,

Repair Time in Hours	Months Since Last Service	Type of Repair	Repairperson
2.9	2	Electrical	Dave Newton
3	6	Mechanical	Dave Newton
4.8	8	Electrical	Bob Jones
1.8	3	Mechanical	Dave Newton
2.9	2	Electrical	Dave 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	Dave Newton

Repair Time is the dependent variable and other three are the independent variables.

We study regression of 'Repair Time' on other three or we use other three to estimate 'Repair Time'.

a. At the .05 level, are there significant relationship between the dependent variable and the independent variables?

Ho: The model is not significant or b0 = b1 = b2 = b3 = 0

H1: The model is significant or atleast 1 bi is not equal to 0.

For this, we will run multiple linear regression and will apply ANOVA test to see if the relationship is significant.

Let us take, Electrical = 1, Mechanical = 0 , Bob Jones = 0 and Dave Newton = 1. (mandatory step for excel)

Steps in Excel:

Input Data > Data > Data Analysis > Regression > Input 'Repair Time' as Y > Input 'other 3' as X > OK

Data (this should be your data):

Repair Time in Hours	Months Since Last Service	Type of Repair	Repairperson
2.9	2	1	1
3	6	0	1
4.8	8	1	0
1.8	3	0	1
2.9	2	1	1
4.9	7	1	0
4.2	9	0	0
4.8	8	0	0
4.4	4	1	0
4.5	6	1	1

Output:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.948789
R Square	0.9002	Part b.
Adjusted R Square	0.8503	Part c.
Standard Error	0.417434
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	3	9.430492	3.143497	18.04002	0.002091
Residual	6	1.045508	0.174251
Total	9	10.476
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.86016	0.728634	2.552942	0.043319	0.077257	3.643064	0.077257	3.643064
X Variable 1	0.291444	0.083598	3.486238	0.013043	0.086886	0.496002	0.086886	0.496002
X Variable 2	1.102406	0.303344	3.634176	0.010911	0.36015	1.844663	0.36015	1.844663
X Variable 3	-0.60909	0.38793	-1.5701	0.167444	-1.55832	0.34014	-1.55832	0.34014

F = 18.04 and p-value = 0.0021 < 0.05, so we reject Ho or can say that the Model or this regression is significant.

b. What is the multiple coefficient of determination?

R Square

0.9002

c. What is the adjusted multiple coefficient of determination?

Adjusted R Square

0.8503

d. Interpret the results.

• F = 18.04 and p-value = 0.0021 < 0.05, so we reject Ho or can say that the Model or this regression is significant.
• R-square = 0.9002 or the model explains 90.02% variability in 'Repair Time'
• Model Equation: Repair Time = 1.86 + 0.29 Months + 1.1 Type - 0.61 Person
• From p-value of each variable, expect 'Repair Person' all are significant as p-value < 0.05.

Please rate my answer and comment for doubt.