25 May Question 91) An air conditioning and heating repair firm c
Question
91) An air conditioning and heating repair firm conducted a study to determine if the average outside temperature could be used to predict the cost of an electric bill for homes during the winter months in Houston, Texas. The resulting regression equation was:
Y = 227.19 – 1.45X, where Y = monthly cost, X = average outside air temperature
(a) If the temperature averaged 48 degrees during December, what is the forecasted cost of December’s electric bill?
(b) If the temperature averaged 38 degrees during January, what is the forecasted cost of January’s electric bill?
92) A large school district is reevaluating its teachers’ salaries. They have decided to use regression analysis to predict mean teachers’ salaries at each elementary school. The researcher uses years of experience to predict salary. The resulting equation was:
Y = 23,313.22 + 1,210.89X, where Y = salary and X = years of experience
(a) If a teacher has 10 years of experience, what is the forecasted salary?
(b) If a teacher has 5 years of experience, what is the forecasted salary?
(c) Based on this equation, for every additional year of service, a teacher could expect his or her salary to increase by how much?
93) An air conditioning and heating repair firm conducted a study to determine if the average outside temperature, thickness of the insulation, and age of the heating 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 = average temperature, X2 = insulation thickness, and X3 = age of heating equipment
(a) If December has an average temperature of 45 degrees and the heater is 2 years old with insulation that is 6 inches thick, what is the forecasted monthly electric bill?
(b) If January has an average temperature of 40 degrees and the heating equipment is 12 years old with insulation that is 2 inches thick, what is the forecasted monthly electric bill?
94) A large school district is reevaluating its teachers’ salaries. They have decided to use regression analysis to predict mean teacher salaries at each elementary school. The researcher uses years of experience to predict salary. The raw data is given in the table below. The resulting equation was:
Y = 19389.21 + 1330.12X, where Y = salary and X = years of experience
Salary
Yrs Exp
$24,265.00
8
$27,140.00
5
$22,195.00
2
$37,950.00
15
$32,890.00
11
$40,250.00
14
$36,800.00
9
$30,820.00
6
$44,390.00
21
$24,955.00
2
$18,055.00
1
$23,690.00
7
$48,070.00
20
$42,205.00
16
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