Question 1

The cubic regression model allows for ________ change(s) in slope.

Accepted Answer

two

Question 2

In which of the following models does the slope coefficient b1 measure the approximate percentage change in   when x increases by 1%?

Accepted Answer

A)  Linear regression model 
B)  Exponential regression model 
C)  Logarithmic regression model 
D)  Log-log regression model 
A)  Linear regression model 
B)  Exponential regression model 
C)  Logarithmic regression model 
D)  Log-log regression model D

Question 3

Thirty employed single individuals were randomly selected to examine the relationship between their age (Age) and their credit card debt (Debt) expressed as a percentage of their annual income. Three polynomial models were applied and the following table summarizes Excel's regression results.   For the cubic model, Debt = β0+ β1Age + β2Age2+ β3Age3+ ε, the following Excel partial output is available. What is the conclusion when testing the individual significance of Age3?

Accepted Answer

Do not reject H_0: β₃ = 0; we cannot conclude Age³ is significant. We cannot conclude that the cubic model is better than the quadratic model.

Question 4

To compute the coefficient of determination R2 we have to use Excel's ________ function first to compute the correlation between y and   .

Accepted Answer

Question 5

The scatterplot shown below represents a typical shape of a cubic regression model y = β0 + β1x + β2x2 + β3x3 + ε.   Which of the following is a predicted value   if x is equal to 12?

Accepted Answer

A)  31.873 
B)  38.173 
C)  37.183 
D)  33.871 
A)  31.873 
B)  38.173 
C)  37.183 
D)  33.871

Question 6

The curve representing the regression equation   = b0 + b1x + b2x2 has a U-shape if b2 < 0.

Accepted Answer

A) True 
 B)False

Question 7

Typically, the sales volume declines with an increase of a product price. It has been observed, however, that for some luxury goods the sales volume may increase when the price increases. The following scatterplot illustrates this rather unusual relationship.   For which of the following two prices are the sales predicted by the quadratic regression equation equal 1700 units?

Accepted Answer

A)  60.51 and 150.15 
B)  61.51 and 151.15 
C)  62.51 and 152.15 
D)  63.51 and 153.15 
A)  60.51 and 150.15 
B)  61.51 and 151.15 
C)  62.51 and 152.15 
D)  63.51 and 153.15

Question 8

The fit of the regression equations   = b0 + b1x + b2x2 and   = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2.

Accepted Answer

A) True 
 B)False

Question 9

For the exponential model ln(y) = β0 + β1x + ε, if x increases by one unit, then E(y) changes by approximately

Accepted Answer

A)  β1 × 100% 
B)  β1 × 100 units 
C)  β1% 
D)  β1 units 
A)  β1 × 100% 
B)  β1 × 100 units 
C)  β1% 
D)  β1 units

Question 10

Typically, the sales volume declines with an increase of a product price. It has been observed, however, that for some luxury goods the sales volume may increase when the price increases. The following scatterplot illustrates this rather unusual relationship.   For the considered range of the price, the relationship between Price and Sales should be described by a ________.

Accepted Answer

A)  concave function 
B)  hyperbola 
C)  convex function 
D)  linear function 
A)  concave function 
B)  hyperbola 
C)  convex function 
D)  linear function

Question 11

For the quadratic equation   = b0 + b1x + b2x2, which of the following expressions must be zero in order to minimize or maximize the predicted y?

Accepted Answer

A)  b1 + 2b2x 
B)  2b1 + b2x 
C)  -b1/2b2  
D)  -b2/2b2 
A)  b1 + 2b2x 
B)  2b1 + b2x 
C)  -b1/2b2  
D)  -b2/2b2

Question 12

The logarithmic and log-log models, y = β0 + β1ln(x) + ε and ln(y) = β0 + β1 ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

Accepted Answer

A)  The logarithmic model. 
B)  The log-log model. 
C)  The models are comparable. 
D)  The provided information is not sufficient to make the conclusion. 
A)  The logarithmic model. 
B)  The log-log model. 
C)  The models are comparable. 
D)  The provided information is not sufficient to make the conclusion.

Question 13

Although allowing for nonlinear trends, polynomials are still linear in the ________.

Accepted Answer

A)  response 
B)  explanatory variables 
C)  coefficients 
D)  none of these options 
A)  response 
B)  explanatory variables 
C)  coefficients 
D)  none of these options

Question 14

Which of the following regression models is most likely to provide the best fit for the data represented by the following scatterplot?

Accepted Answer

A)  Exponential model 
B)  Logarithmic model 
C)  Linear model 
D)  Log-log model 
A)  Exponential model 
B)  Logarithmic model 
C)  Linear model 
D)  Log-log model

Question 15

What R function is used to fit a quadratic regression model?

Accepted Answer

A)  lm 
B)  predict 
C)  summary 
D)  cor 
A)  lm 
B)  predict 
C)  summary 
D)  cor

Question 16

The regression model ln(y) = β0 + β1x + ε is called an exponential model.

Accepted Answer

A) True 
 B)False

Question 17

It is believed that the sales volume of one-liter Pepsi bottles depends on the price of the bottle and the price of a one-liter bottle of Coca-Cola. The following data have been collected for a certain sales region.   The linear model Pepsi Sales = β0 + β1Pepsi Price + β2Cola Price + ε and the log-log model ln(Pepsi Sales) = β0 + β1ln(Pepsi Price) + β2ln(Cola Price) + ε have been estimated as follows:   For the log-log model, interpret the estimated coefficient for ln(Pepsi Price).

Accepted Answer

Holding Cola Price constant, t

Question 18

The linear and logarithmic models, y = β0 + β1x + ε and y = β0 + β1 ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

Accepted Answer

A)  The linear model. 
B)  The logarithmic model. 
C)  The models are not comparable. 
D)  The provided information is not sufficient to make the conclusion. 
A)  The linear model. 
B)  The logarithmic model. 
C)  The models are not comparable. 
D)  The provided information is not sufficient to make the conclusion.

Question 19

Thirty employed single individuals were randomly selected to examine the relationship between their age (Age) and their credit card debt (Debt) expressed as a percentage of their annual income. Three polynomial models were applied and the following table summarizes Excel's regression results.   If you impose the restrictions β2 = β3 = 0 on the model Debt = β0 + β1Age + β2Age2 + β3Age3 + ε, what will be the sum of the squared errors (SSER) computed for the restricted model?

Accepted Answer

Question 20

It is believed that the sales volume of one-liter Pepsi bottles depends on the price of the bottle and the price of a one-liter bottle of Coca-Cola. The following data have been collected for a certain sales region.   The linear model Pepsi Sales = β0 + β1Pepsi Price + β2Cola Price + ε and the log-log model ln(Pepsi Sales) = β0 + β1ln(Pepsi Price) + β2ln(Cola Price) + ε have been estimated as follows:   Using Excel or R, which of the two models provides a better fit?

Accepted Answer

The cubic regression model allows for ________ change(s) in slope.

In which of the following models does the slope coefficient b₁ measure the approximate percentage change in when x increases by 1%?

To compute the coefficient of determination R²we have to use Excel's ________ function first to compute the correlation between y and .

The scatterplot shown below represents a typical shape of a cubic regression model y = β₀ + β₁x + β₂x² + β₃x³ + ε. Which of the following is a predicted value if x is equal to 12?

The curve representing the regression equation = b₀ + b₁x + b₂x² has a U-shape if b₂ < 0.

The fit of the regression equations = b₀ + b₁x + b₂x² and = b₀ + b₁x + b₂x² + b₃x³can be compared using the coefficient of determination R².

For the exponential model ln(y) = β₀ + β₁x + ε, if x increases by one unit, then E(y) changes by approximately

For the quadratic equation = b₀ + b₁x + b₂x², which of the following expressions must be zero in order to minimize or maximize the predicted y?

The logarithmic and log-log models, y = β₀ + β₁ln(x) + ε and ln(y) = β₀ + β₁ ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

Although allowing for nonlinear trends, polynomials are still linear in the ________.

Which of the following regression models is most likely to provide the best fit for the data represented by the following scatterplot?

What R function is used to fit a quadratic regression model?

The regression model ln(y) = β₀ + β₁x + ε is called an exponential model.

The linear and logarithmic models, y = β₀ + β₁x + ε and y = β₀ + β₁ ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Exam 16: Regression Models for Nonlinear Relationships

The cubic regression model allows for ________ change(s) in slope.

In which of the following models does the slope coefficient b1 measure the approximate percentage change in when x increases by 1%?

To compute the coefficient of determination R2 we have to use Excel's ________ function first to compute the correlation between y and .

The scatterplot shown below represents a typical shape of a cubic regression model y = β0 + β1x + β2x2 + β3x3 + ε. Which of the following is a predicted value if x is equal to 12?

The curve representing the regression equation = b0 + b1x + b2x2 has a U-shape if b2 < 0.

The fit of the regression equations = b0 + b1x + b2x2 and = b0 + b1x + b2x2 + b3x3 can be compared using the coefficient of determination R2.

For the exponential model ln(y) = β0 + β1x + ε, if x increases by one unit, then E(y) changes by approximately

For the quadratic equation = b0 + b1x + b2x2, which of the following expressions must be zero in order to minimize or maximize the predicted y?

The logarithmic and log-log models, y = β0 + β1ln(x) + ε and ln(y) = β0 + β1 ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

Although allowing for nonlinear trends, polynomials are still linear in the ________.

Which of the following regression models is most likely to provide the best fit for the data represented by the following scatterplot?

What R function is used to fit a quadratic regression model?

The regression model ln(y) = β0 + β1x + ε is called an exponential model.

The linear and logarithmic models, y = β0 + β1x + ε and y = β0 + β1 ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling and Sampling Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

In which of the following models does the slope coefficient b₁ measure the approximate percentage change in when x increases by 1%?

To compute the coefficient of determination R²we have to use Excel's ________ function first to compute the correlation between y and .

The scatterplot shown below represents a typical shape of a cubic regression model y = β₀ + β₁x + β₂x² + β₃x³ + ε. Which of the following is a predicted value if x is equal to 12?

The curve representing the regression equation = b₀ + b₁x + b₂x² has a U-shape if b₂ < 0.

The fit of the regression equations = b₀ + b₁x + b₂x² and = b₀ + b₁x + b₂x² + b₃x³can be compared using the coefficient of determination R².

For the exponential model ln(y) = β₀ + β₁x + ε, if x increases by one unit, then E(y) changes by approximately

For the quadratic equation = b₀ + b₁x + b₂x², which of the following expressions must be zero in order to minimize or maximize the predicted y?

The logarithmic and log-log models, y = β₀ + β₁ln(x) + ε and ln(y) = β₀ + β₁ ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?

The regression model ln(y) = β₀ + β₁x + ε is called an exponential model.

The linear and logarithmic models, y = β₀ + β₁x + ε and y = β₀ + β₁ ln(x) + ε, were fit given data on y and x, and the following table summarizes the regression results. Which of the two models provides a better fit?