76) Which of the following statements provides the best guidance for model building?
A) If the value of r2 increases as more variables are added to the model, the variables should remain in the model,
regardless of the magnitude of increase.
B) If the value of the adjusted r2 increases as more variables are added to the model, the variables should remain
in the model.
C) If the value of r2 increases as more variables are added to the model, the variables should not remain in the
model, regardless of the magnitude of the increase.
D) If the value of the adjusted r2 increases as more variables are added to the model, the variables should not
remain in the model.
E) None of the statements provide accurate guidance.
77) An automated process to systematically add or delete independent variables from a regression model is
known as
A) nonlinear transformations.
B) multicollinearity.
C) multiple regression.
D) least squares method.
E) None of the above
78) Which of the following is not a common pitfall of regression?
A) If the assumptions are not met, the statistical tests may not be valid.
B) Nonlinear relationships cannot be incorporated.
C) Two variables may be highly correlated to one another but one is not causing the other to change.
D) Concluding that a statistically significant relationship implies practical value.
E) Using a regression equation beyond the range of X is very questionable.
79) The condition of an independent variable being correlated to one or more other independent variables is
referred to as
A) multicollinearity.
B) statistical significance.
C) linearity.
D) nonlinearity.
E) The significance level for the F–test is not valid.
80) Which of the following is true regarding a regression model with multicollinearity, a high r2 value, and a low
F–test significance level?
A) The model is not a good prediction model.
B) The high value of r2 is due to the multicollinearity.
C) The interpretation of the coefficients is valuable.
D) The significance level tests for the coefficients are not valid.
E) The significance level for the F–test is not valid.
81) 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?
82) 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?
83) 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?
84) 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?
85) 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.
86) 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.
87) 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?
88) Consider the regression model Y = 389.10 – 14.6X. If the r2 value is 0.657, what is the correlation coefficient?
89) 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 variables are number of
family members and insurance type (government funded, private insurance and other). He has coded insurance
type as the following:
X2 = 1 if government funded, X3 = 1 if private insurance
Below is his Excel output.
(a) What is the prediction equation?
(b) Based on the significance F–test, is this model a good prediction equation?
(c) What percent of the variation in medical expenses is explained by the independent variables?
(d) Based on his model, what are the predicted monthly expenses for a family of four with private insurance?
(e) Based on his model, what are the predicted monthly expenses for a family of two with government
funded insurance?
(f) Based on his model, what are the predicted monthly expenses for a family of five with no insurance?
90) 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 would like to examine the significance of
a following quadratic model for predicting salary based on years of experience.
Y = β0 + β1X1 + β2X2 + ε where X1 = Yrs Exp and X2 = Yrs Exp2
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) What is the adjusted r2?
(b) What is the prediction equation?
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 a home during the winter months in
Richmond, VA. It was determined that a quadratic model could be used and the following prediction equation
was established:
Y = $1557.76 – 55.05X1 + 0.56X2
where Y = monthly cost, X1 = average temperature, and X2 = average temperature2
(a) If December has an average temperature of 43 degrees what is the forecasted monthly electric bill?
(b) If January has an average temperature of 40 degrees what is the forecasted monthly electric bill?
92) 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 research has come up with the following prediction
equation:
Y = $18012.24 + 1432.37X1 – 4.07 X2 where X1 = Yrs Exp and X2 = Yrs Exp2
(a) If a teacher has 7 years of experience, what is the expected salary?
(b) If teacher has 10 years of experience, what is the expected salary?
93) In regression, the variable to be predicted is called the ________ variable.
94) Explain the purposes of regression models.
95) Describe the purpose and structure of a scatter diagram.
96) In regression, the X variable is known as the ________ variable.
97) What is the formula for r2?
98) If every point lies on the regression line, r2 = ________.
99) The regression line minimizes the sum of the ________.
100) The ________ measures the total variability in Y about the mean.
101) The ________ measures the variability in Y about the regression line.
102) The ________ indicates how much total variability in Y is explained by the regression model.
104) Explain what r2 is.
105) What can be said about an r2 value of 0.96?
106) Explain what the correlation coefficient is.
107) What can be said about a correlation coefficient of –1?
108) What can be said about a correlation coefficient of +1?
109) Another name for the “Multiple R” that is given in Excel is ________.
110) Describe a residual plot.
111) The standard deviation of the regression is also called ________.
112) List the four assumptions of the regression model.
113) What is the difference between simple linear regression models and multiple regression models?
114) To include qualitative data in regression analysis, you must first create a ________ variable.
115) For each qualitative variable, he number of dummy variables must equal ________ the number of categories
of the qualitative variable.
116) As more variables are added to the model, what happens to the r2 value?
117) Discuss the relationship between r2 and adjusted r2.
118) When the independent variables are correlated with each other, ________ is said to exist.
119) With a nonlinear relationship, a ________ is necessary to turn a nonlinear model into a linear model.
120) List four pitfalls of regression.