Chapter 4 Regression Models

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

(a) Develop a scatter diagram.

(b) What is the correlation coefficient?

(c) What is the coefficient of determination?

95) A large international sales organization has collected data on the number of employees and the annual gross sales during the last 7 years.

# of employees	sales (in $000s)
1975	100
2010	110
2005	122
2020	130
2030	139
2031	152
2050	164
2100	?

(a) Develop a scatter diagram.

(b) Determine the correlation coefficient.

(c) Determine the coefficient of determination.

(d) Determine the least squares trend line.

(e) Determine the predicted value of sales for 2100 employees.

96) A large department store has collected the following monthly data on lost sales revenue due to theft and the number of security guard hours on duty:

Lost Sales Revenue ($000s)	Total Security Guard hours	Lost Sales Revenue ($000s)	Total Security Guard hours
1.0	600	1.8	950
1.4	630	2.1	1300
1.9	1000	2.3	1350
2.0	1200

(a) Determine the least squares regression equation.

(b) Using the results of part (a), find the estimated lost sales revenues if the total number of security guard hours is 800.

(c) Calculate the coefficient of correlation.

(d) Calculate the coefficient of determination.

97) Bob White is conducting research on monthly expenses for medical care, including over-the-counter medicine. His dependent variable is monthly expenses for medical care while his independent variable is number of family members. Below is his Excel output.

(a) What is the prediction equation?

(b) Based on his model, each additional family member increases the predicted costs by how much?

(c) Based on the significance F-test, is this model a good prediction equation?

(d) What percent of the variation in medical expenses is explained by the size of the family?

(e) Can the null hypothesis that the slope is zero be rejected? Why or why not?

(f) What is the value of the correlation coefficient?

98) An electronics company is looking to develop a regression model to predict the number of units sold for a special running watch. Data is provided below:

Sales (units)	Price ($)	Advertising ($)
500	100	50
480	120	40
485	110	45
510	103	55
490	108	40
488	109	30
496	106	45

Use model building to determine the best prediction equation for Sales, based on highest adjusted r2.

99) An electronics company is looking to develop a regression model to predict the number of units sold for a special running watch. Data is provided below:

Sales (units)	Price ($)	Advertising ($)	Holiday
500	100	50	Yes
480	120	40	Yes
485	110	45	No
510	103	55	Yes
490	108	40	No
488	109	30	No
496	106	45	Yes

A) Define the dummy variable(s) for the regression model.

B) What is the correlation between the Holiday categorical variable and sales?

100) A study was done to determine the relationship between GPA and starting salaries for college graduates. The data is shown in the table below:

Starting Salary ($)	GPA	GPA2
35,000	2.5	6.25
37,000	2.7	7.29
38,000	2.8	7.84
55,000	3.5	12.25
60,000	3.6	12.96
65,000	3.7	13.69
80,000	3.9	15.21

Use model building to determine the best fit based on highest adjusted r2.