An air conditioning and heating repair firm conducted a study to determine if th
ID: 3209583 • Letter: A
Question
An air conditioning and heating repair firm conducted a study to determine if the outside temperature, thickness of the insulation, and age of the equipment could be used to predict the electric bill for a home during the winter months in Houston, Texas. The resulting regression equation was:
Y = 256.89 – 1.45X1 –11.26X2 +6.10X3, where Y = monthly cost, X1 = temperature, X2 = insulation thickness, X3 = age of equipment
1. The above is a single linear regression model.
T/F
2. The model should be classified as deterministic.
T/F
3. Monthly cost is the independent variable.
T/F
4. According to the above model, an increase 1 degree of average temperature will result in a decrease of 1.45 in average monthly cost.
T/F
5. According to the above model, an decrease 1 degree of average temperature will result in a decrease of 1.45 in average monthly cost.
T/F
6. What is the slope for temperature?
11.26
-11.26
256.89
-256.89
6.10
-6.10
-1.45
1.45
Unknown
7. What is the sum of the squared error?
256.89
11.26
-11.26
-6.10
Unknown
-256.89
1.45
6.10
-1.45
8. If December has an average temperature of 25 degrees and the heater is 2 years old with insulation that is 6 inches thick, what is the forecasted monthly electric bill?
234.72
372.90
205.72
165.28
136.28
250.76
401.90
11.26
-11.26
256.89
-256.89
6.10
-6.10
-1.45
1.45
Unknown
7. What is the sum of the squared error?
256.89
11.26
-11.26
-6.10
Unknown
-256.89
1.45
6.10
-1.45
8. If December has an average temperature of 25 degrees and the heater is 2 years old with insulation that is 6 inches thick, what is the forecasted monthly electric bill?
234.72
372.90
205.72
165.28
136.28
250.76
401.90
Explanation / Answer
1. The above is a single linear regression model. False
As this model as multiple dependent variable (: temperature, thickness of the insulation, and age of the equipment) to predict the independent variable: (electric bill)
2. The model should be classified as deterministic.False.
Regression is a predictive model
3. Monthly cost is the independent variable. False
The mothly cost depends on independent variables: temperature, thickness of the insulation, and age of the equipment
4.According to the above model, an increase 1 degree of average temperature will result in a decrease of 1.45 in average monthly cost.
True. Because coefficient of the temperature in the regression equation : -1.45
5. According to the above model, an decrease 1 degree of average temperature will result in a decrease of 1.45 in average monthly cost.
False Because coefficient of the temperature in the regression equation : -1.45 which is negative as temperature increases cost decreses.
6. What is the slope for temperature? Ans : -1.45 : Coefficient of the indepenent variable temperature in the equation
7.What is sum of squared of error? Unknown With the just the regresssion equation the sum of squared error can not be found
8. If December has an average temperature of 25 degrees and the heater is 2 years old with insulation that is 6 inches thick, what is the forecasted monthly electric bill?
Given average temperature of 25 degrees; Temperture X1 = 25
the heater is 2 years old i.e Heater age X2 =2 years
insulation that is 6 inches thick ; insulation thickness X3 = 6 inches
Substitute the above values in the given regression equation.
Y = 256.89 – 1.45X1 –11.26X2 +6.10X3, where Y = monthly cost, X1 = temperature, X2 = insulation thickness, X3 = age of equipment
Y = 256.89 - 1.45 x 25 - 11.26 x 6 + 6.10 x 2 = 256.89 - 36.25 - 67.56 + 12.20 = 165.28
Ans : 165.28
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