Mulberry Realty sells homes in the northeast section of the United States. A frequently asked question by prospective buyers is: If we buy this house, how much can we expect to pay to heat it during the winter? The research division of Mulberry is asked to develop some guidelines for heating costs (Cost) (measured in $) for single family homes. The division decides three variables are related to heating costs: (1) the mean daily outside temperature (Temp) (in degrees Fahrenheit); (2) the number of inches of attic insulation (Insulation); and (3) the age of the furnace in the house (Age) (measured in years). The division collected data during the month of January for a sample of homes. Parentheses contain the variable names (in bold) as listed in the data set.
The data set for this scenario is included in an Excel file.
a. Is the information used in this analysis, cross-sectional data or time series data? (4 pts)
b. State your a priori hypothesis about the sign of the slope for each independent variable. (3 pts each)
c. Write out the estimated regression equation using variable specific names? (5 pts)
d. Interpret the slope coefficient for the variable with the largest slope coefficient. (5 pts)
e. For the slope coefficient with the smallest value (in absolute value), test to see if it has the directional relationship hypothesized in part (b). Alpha = 0.05. (15 pts)
Data Set:
Cost ($)
Temp (deg)
Insulation (ins.)
Age (yrs)
250
35
3
6
360
29
4
10
165
36
7
3
43
60
6
9
92
65
5
6
200
30
5
5
355
10
6
7
290
7
10
10
230
21
9
11
120
55
2
5
73
54
12
4
205
48
5
1
400
20
5
15
320
39
4
7
72
60
8
6
272
20
5
8
94
58
7
3
190
40
8
11
235
27
9
8
139
30
7
5
Mulberry Realty sells homes in the northeast section of the United States. A frequently asked question by prospective buyers is: If we buy this house, how much can we expect to pay to heat it during the winter? The research division of Mulberry is asked to develop some guidelines for heating costs (Cost) (measured in $) for single family homes. The division decides three variables are related to heating costs: (1) the mean daily outside temperature (Temp) (in degrees Fahrenheit); (2) the number of inches of attic insulation (Insulation); and (3) the age of the furnace in the house (Age) (measured in years). The division collected data during the month of January for a sample of homes. Parentheses contain the variable names (in bold) as listed in the data set.
The data set for this scenario is included in an Excel file.
a. Is the information used in this analysis, cross-sectional data or time series data? (4 pts)
b. State your a priori hypothesis about the sign of the slope for each independent variable. (3 pts each)
c. Write out the estimated regression equation using variable specific names? (5 pts)
d. Interpret the slope coefficient for the variable with the largest slope coefficient. (5 pts)
e. For the slope coefficient with the smallest value (in absolute value), test to see if it has the directional relationship hypothesized in part (b). Alpha = 0.05. (15 pts)
Data Set:
| Cost ($) | Temp (deg) | Insulation (ins.) | Age (yrs) |
| 250 | 35 | 3 | 6 |
| 360 | 29 | 4 | 10 |
| 165 | 36 | 7 | 3 |
| 43 | 60 | 6 | 9 |
| 92 | 65 | 5 | 6 |
| 200 | 30 | 5 | 5 |
| 355 | 10 | 6 | 7 |
| 290 | 7 | 10 | 10 |
| 230 | 21 | 9 | 11 |
| 120 | 55 | 2 | 5 |
| 73 | 54 | 12 | 4 |
| 205 | 48 | 5 | 1 |
| 400 | 20 | 5 | 15 |
| 320 | 39 | 4 | 7 |
| 72 | 60 | 8 | 6 |
| 272 | 20 | 5 | 8 |
| 94 | 58 | 7 | 3 |
| 190 | 40 | 8 | 11 |
| 235 | 27 | 9 | 8 |
| 139 | 30 | 7 | 5 |
