Deck 12: Multiple Regression and Model Building

Question 1

A statistics professor gave three quizzes leading up to the first test in his class. The quiz
grades and test grade for each of eight students are given in the table.

Answer 1

Question 2

Answer 2

D

Question 3

Answer 3

D

Question 4

Question 5

A first-order model may include terms for both quantitative and qualitative independent
variables.

Question 6

Probabilistic models that include more than one dependent variable are called multiple regression
models.

Question 7

Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:

Question 8

It is safe to conduct t-tests on the individual β parameters in a first-order linear model in order to
determine which independent variables are useful for predicting y and which are not.

Question 9

As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS)majors in a particular year. The researchers were interested in modeling y, a studentʹs grade
Point average (GPA)after three semesters, as a function of the following independent variables
(recorded at the time the students enrolled in the university):

Question 10

The method of fitting first-order models is the same as that of fitting the simple straight-line
model, i.e. the method of least squares.

Question 11

Why is the random error term ε added to a multiple regression model?

Question 12

For a multiple regression model, we assume that the mean of the probability distribution of the
random error is 0.

Question 13

Question 14

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 15

A term that contains the value of a quantitative variable raised to the second power is called a
higher-order term.

Question 16

A qualitative variable whose outcomes are assigned numerical values is called a coded variable.

Question 17

Retail price data for n = 60 hard disk drives were recently reported in a computer
magazine. Three variables were recorded for each hard disk drive:

Question 18

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 19

A first-order model does not contain any higher-order terms.

Question 20

Question 21

Question 22

As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS)majors in a particular year. The researchers were interested in modeling y, a studentʹs grade
Point average (GPA)after three semesters, as a function of the following independent variables
(recorded at the time the students enrolled in the university):

Question 23

The rejection of the null hypothesis in a global F-test means that the model is the best model for
providing reliable estimates and predictions.

Question 24

As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS)majors in a particular year. The researchers were interested in modeling y, a studentʹs grade
Point average (GPA)after three semesters, as a function of the following independent variables
(recorded at the time the students enrolled in the university):

Question 25

Retail price data for n = 60 hard disk drives were recently reported in a computer
magazine. Three variables were recorded for each hard disk drive:

Question 26

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 27

The confidence interval for the mean E(y)is narrower that the prediction interval for y.

Question 28

The table below shows data for n = 20 observations.

Question 29

Question 30

Question 31

Retail price data for n = 60 hard disk drives were recently reported in a computer
magazine. Three variables were recorded for each hard disk drive:

Question 32

A statistics professor gave three quizzes leading up to the first test in his class. The quiz
grades and test grade for each of eight students are given in the table.

Question 33

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 34

Question 35

As part of a study at a large university, data were collected on n = 224 freshmen computer
science (CS)majors in a particular year. The researchers were interested in modeling y, a
studentʹs grade point average (GPA)after three semesters, as a function of the following
independent variables (recorded at the time the students enrolled in the university):

Question 36

Question 37

As part of a study at a large university, data were collected on n = 224 freshmen computer
science (CS)majors in a particular year. The researchers were interested in modeling y, a
studentʹs grade point average (GPA)after three semesters, as a function of the following
independent variables (recorded at the time the students enrolled in the university):

Question 38

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 39

Question 40

As part of a study at a large university, data were collected on n = 224 freshmen computer science (CS)majors in a particular year. The researchers were interested in modeling y, a studentʹs grade
Point average (GPA)after three semesters, as a function of the following independent variables
(recorded at the time the students enrolled in the university):

Question 41

We decide to conduct a multiple regression analysis to predict the attendance at a major league baseball game. We use the size of the stadium as a quantitative independent variable and the type
Of game as a qualitative variable (with two levels - day game or night game). We hypothesize the
Following model:

Question 42

Consider the partial printout below.

Question 43

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 44

Question 45

Question 46

One of three surfaces is produced by a complete second-order model with two quantitative
independent variables: a paraboloid that opens upward, a paraboloid that opens downward, or a
saddle-shaped surface.

Question 47

Retail price data for n = 60 hard disk drives were recently reported in a computer magazine. Three variables were recorded for each hard disk drive:

Question 48

A college admissions officer proposes to use regression to model a studentʹs college GPA
at graduation in terms of the following two variables: The admissions officer believes the relationship between college GPA and high school
GPA is linear and the relationship between SAT score and college GPA is linear. She also
believes that the relationship between college GPA and high school GPA depends on the
studentʹs SAT score. Write the regression model she should fit.

Question 49

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 50

A college admissions officer proposes to use regression to model a studentʹs college GPA
at graduation in terms of the following two variables:
x1 = high school GPA
x2 = SAT score
The admissions officer believes the relationship between college GPA and high school
GPA is linear and the relationship between SAT score and college GPA is linear. She also
believes that the relationship between college GPA and high school GPA depends on the
studentʹs SAT score. She proposes the regression model: Explain how to determine if the relationship between college GPA and SAT score depends
on the high school GPA.

Question 51

Question 52

The complete second-order model with two quantitative independent variables does not allow for
interaction between the two independent variables.

Question 53

Question 54

Which equation represents a complete second-order model for two quantitative independent variables?

Question 55

A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant)rate. Thus, the
Model proposed to best explain auction price (y, in dollars)by number of bidders (x)is the
Quadratic model

Question 56

Question 57

Question 58

The concessions manager at a beachside park recorded the high temperature, the number
of people at the park, and the number of bottles of water sold for each of 12 consecutive
Saturdays. The data are shown below.

Question 59

Question 60

Question 61

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that
When the gem is valued at very high prices, the demand increases with price due to the status the
Owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the
Demand for the gem by its price is the quadratic model

Question 62

Consider the data given in the table below. Plot the data on a scattergram. Does a second-order model seem to be a good fit for the data? Explain.

Question 63

Consider the data given in the table below.

Question 64

Question 65

Question 66

The table shows the profit y (in thousands of dollars)that a company made during a
month when the price of its product was x dollars per unit.

Question 67

Question 68

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for low prices, the demand decreases as the price of the gem increases. However, experts hypothesize that
When the gem is valued at very high prices, the demand increases with price due to the status the
Owners believe they gain by obtaining the gem. Thus, the model proposed to best explain the
Demand for the gem by its price is the quadratic model where y = Demand (in thousands)and x = Retail price per carat (dollars).
This model was fit to data collected for a sample of 12 rare gems.

Question 69

What relationship between x and y is suggested by the scattergram?

Question 70

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for
low prices, the demand decreases as the price of the gem increases. However, experts
hypothesize that when the gem is valued at very high prices, the demand increases with
price due to the status the owners believe they gain by obtaining the gem. Thus, the model
proposed to best explain the demand for the gem by its price is the quadratic model where y = Demand (in thousands)and x = Retail price per carat (dollars).
This model was fit to data collected for a sample of 12 rare gems. A portion of the printout
is given below:

Question 71

A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant)rate. Thus, the
Model proposed to best explain auction price (y, in dollars)by number of bidders (x)is the
Quadratic model

Question 72

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 73

Question 74

A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant)rate. Thus, the
Model proposed to best explain auction price (y, in dollars)by number of bidders (x)is the
Quadratic model

Question 75

A certain type of rare gem serves as a status symbol for many of its owners. In theory, for
low prices, the demand decreases as the price of the gem increases. However, experts
hypothesize that when the gem is valued at very high prices, the demand increases with
price due to the status the owners believe they gain by obtaining the gem. Thus, the model
proposed to best explain the demand for the gem by its price is the quadratic model

Question 76

When modeling E(y)with a single qualitative independent variable, the number of 01 dummy
variables in the model is equal to the number of levels of the qualitative variable.

Question 77

A study of the top MBA programs attempted to predict the average starting salary (in $1000ʹs)of graduates of the program based on the amount of tuition (in $1000ʹs)charged by the program and
The average GMAT score of the programʹs students. The results of a regression analysis based on a
Sample of 75 MBA programs is shown below:

Question 78

Question 79

Consider the second-order model

Question 80

A collector of grandfather clocks believes that the price received for the clocks at an auction increases with the number of bidders, but at an increasing (rather than a constant)rate. Thus, the
Model proposed to best explain auction price (y, in dollars)by number of bidders (x)is the
Quadratic model