1) Note: This is a continuation of problem 4 on HW7. Salsberry Realty sells home
ID: 3170718 • Letter: 1
Question
1) Note: This is a continuation of problem 4 on HW7. Salsberry Realty sells homes along the east coast of the United States. One of the questions most frequently asked by prospective buyers is: If we purchase this home, how much can we expect to pay to heat it during the winter? The research department at Salsberry has been asked to develop some guidelines regarding heating costs for single-family homes. They put together a dataset for 20 homes that appears in the Home Heating worksheet of the HW8 data workbook on Moodle. The dataset contains the following variables: Cost – Cost to heat the home last January, Temperature – The mean daily outside temperature for the home last January, and Insulation – the number of inches of insulation in the attic.
a) Use Excel to fit the multiple regression model using Cost as the Y variable and the other two variables as the X or independent variables. Is the model statistically significant at = 0.05?
b) Provide a point prediction for a house with 3 inches of insulation in the attic and an average January temperature of 20 degrees.
c) Provide an approximate 90% prediction interval for a house with 3 inches of insulation in the attic and an average January temperature of 20 degrees.
Cost Temperature Insulation 250 35 3 360 29 4 165 36 7 43 60 6 92 65 5 200 30 5 355 10 6 290 7 10 230 21 9 120 55 2 73 54 12 205 48 5 400 20 5 320 39 4 72 60 8 272 20 5 94 58 7 190 40 8 235 27 9 139 30 7Explanation / Answer
Result:
1) Note: This is a continuation of problem 4 on HW7. Salsberry Realty sells homes along the east coast of the United States. One of the questions most frequently asked by prospective buyers is: If we purchase this home, how much can we expect to pay to heat it during the winter? The research department at Salsberry has been asked to develop some guidelines regarding heating costs for single-family homes. They put together a dataset for 20 homes that appears in the Home Heating worksheet of the HW8 data workbook on Moodle. The dataset contains the following variables: Cost – Cost to heat the home last January, Temperature – The mean daily outside temperature for the home last January, and Insulation – the number of inches of insulation in the attic.
a) Use Excel to fit the multiple regression model using Cost as the Y variable and the other two variables as the X or independent variables. Is the model statistically significant at a = 0.05?
Regression Analysis
R²
0.776
Adjusted R²
0.749
n
20
R
0.881
k
2
Std. Error
52.982
Dep. Var.
Cost
ANOVA table
Source
SS
df
MS
F
p-value
Regression
165,194.5213
2
82,597.2607
29.42
3.01E-06
Residual
47,721.2287
17
2,807.1311
Total
212,915.7500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
90% lower
90% upper
Intercept
490.2859
44.4098
11.040
3.56E-09
413.0303
567.5416
Temperature
-5.1499
0.7019
-7.337
1.16E-06
-6.3709
-3.9289
Insulation
-14.7181
4.9339
-2.983
.0084
-23.3012
-6.1351
The regression line
Cost = 490.2859 -5.1499* Temperature --14.7181*Insulation
Calculated F=29.42, P=0.0000 which is < 0.05 level of significance.
The model statistically significant.
b) Provide a point prediction for a house with 3 inches of insulation in the attic and an average January temperature of 20 degrees.
Predicted values for: Cost
90% Confidence Interval
90% Prediction Interval
Temperature
Insulation
Predicted
lower
upper
lower
upper
Leverage
20
3
343.134
300.508
385.760
241.586
444.682
0.214
Predicted cost = 343.13
c) Provide an approximate 90% prediction interval for a house with 3 inches of insulation in the attic and an average January temperature of 20 degrees.
90% prediction interval = (241.59, 444.68)
Regression Analysis
R²
0.776
Adjusted R²
0.749
n
20
R
0.881
k
2
Std. Error
52.982
Dep. Var.
Cost
ANOVA table
Source
SS
df
MS
F
p-value
Regression
165,194.5213
2
82,597.2607
29.42
3.01E-06
Residual
47,721.2287
17
2,807.1311
Total
212,915.7500
19
Regression output
confidence interval
variables
coefficients
std. error
t (df=17)
p-value
90% lower
90% upper
Intercept
490.2859
44.4098
11.040
3.56E-09
413.0303
567.5416
Temperature
-5.1499
0.7019
-7.337
1.16E-06
-6.3709
-3.9289
Insulation
-14.7181
4.9339
-2.983
.0084
-23.3012
-6.1351
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