Question

2) The manager of a physical plant department at a regional Midwestern university is interested in reducing the average time to completion of routine work orders. The time to completion is defined as the difference between the date of receipt of a work order and the date closing information is entered. The number of labor hours charged to each work order, the cost of materials and building type (classified into four types on the campus: residence halls, athletic, academic, and administrative) are variables believed to be related to the time to completion of the work order. The manager also constructed the interaction of Hours and Material and the quadratic term Hours2. A random sample of 72 work orders was obtained. These data appear in the worksheet titled University data in workbook HW7 data on Moodle.

a) Fit a multiple regression model using Days as the Y or dependent variable with independent variables of Hours, Material, and the Hours^2 quadratic term. Is the model significant at a= 0.05? What is the R-Squared for this model? Interpret the R-Squared value in the context of the problem.

b) Interpret the coefficients of the model in part a) in the context of the problem. Include an assessment of their statistical significance at a= 0.05.

c) Using the model in part a), make a point prediction for the number of days to complete a work order for an administrative building that requires 3 hours, and $20 of material.

d) You determine that the work order initially thought to require 3 hours and $20 material will require an additional $10 in material (an increase from $20 to $30). Using the model in part a) what is the expected change in days to complete the work order?

e) Define Residence Hall as the baseline building and develop indicator variables to include the Building variable in regression models. Fit a multiple regression model using Days as the Y or dependent variable with independent variables of Hours, Material, the Hrs*mat interaction and the building indicators. What is the R-Squared for this model? Interpret the R-Squared value in the context of the problem.

f) Using the model from part e), make a point prediction for the number of days to complete a work order for an administrative building that requires 3 hours, and $20 of material.

g) Using the model from part e), provide a 90% confidence interval on the average number of days to complete a work order for an administrative building that requires 3 hours, and $20 of material.

DATA:

Days	Hours	Material	Building
7	0.50	0	Residence Hall
9	6.50	117	Academic Building
3	1.00	6	Residence Hall
4	0.50	0	Residence Hall
1	1.00	4	Residence Hall
1	1.50	27	Residence Hall
1	0.50	0	Academic Building
1	0.25	0	Academic Building
13	0.50	87	Administrative Building
19	30.00	131	Academic Building
3	0.25	0	Academic Building
6	7.00	18	Administrative Building
0	0.50	0	Residence Hall
1	0.25	0	Residence Hall
2	0.50	0	Administrative Building
2	1.00	6	Residence Hall
1	3.50	6	Residence Hall
1	0.50	0	Residence Hall
1	0.50	0	Academic Building
1	0.25	0	Residence Hall
1	0.25	10	Administrative Building
29	2.75	4	Residence Hall
7	1.00	242	Administrative Building
5	0.25	2	Administrative Building
3	2.50	93	Residence Hall
13	0.50	1	Residence Hall
1	0.50	8	Residence Hall
4	0.25	0	Athletic Building
3	0.50	0	Residence Hall
12	0.25	2	Residence Hall
14	2.00	4	Residence Hall
4	4.00	0	Residence Hall
4	1.00	2	Residence Hall
29	2.00	25	Residence Hall
1	0.50	0	Residence Hall
3	0.50	0	Residence Hall
3	0.50	0	Residence Hall
5	1.00	28	Academic Building
25	0.50	1350	Athletic Building
1	0.50	4	Residence Hall
30	0.50	3	Residence Hall
1	0.75	13	Residence Hall
5	0.50	0	Academic Building
7	0.25	0	Academic Building
10	0.50	0	Academic Building
1	1.00	139	Administrative Building
2	0.25	0	Residence Hall
1	2.00	14	Academic Building
50	11.00	33	Academic Building
4	0.50	4	Administrative Building
3	0.50	0	Residence Hall
5	1.00	0	Academic Building
6	0.25	0	Residence Hall
1	0.45	4	Residence Hall
21	0.50	0	Residence Hall
5	0.50	0	Residence Hall
8	2.00	0	Academic Building
12	1.00	0	Residence Hall
3	0.50	0	Residence Hall
2	0.25	44	Residence Hall
1	0.25	2	Administrative Building
4	0.50	8	Academic Building
3	0.75	6	Residence Hall
1	0.50	0	Athletic Building
1	0.50	0	Administrative Building
1	0.50	0	Residence Hall
1	0.50	4	Residence Hall
3	1.00	10	Academic Building
1	0.50	0	Residence Hall
2	1.00	13	Academic Building
17	1.50	0	Academic Building
3	0.50	1	Academic Building

Answer 1