Question 1

For the model ln(y)= β0 + β1ln(x)+ ε with 0 1 < 1,if x increases than E(y)increases but at a slower rate.

Accepted Answer

A) True 
 B)False

Question 2

In the model ln(y)= β0 + β1ln(x)+ ε,the coefficient β1 is the approximate:

Accepted Answer

A) change in E(y)when x increases by one unit. 
B) percentage change in E(y)when x increases by 1%. 
C) percentage change in E(y)when x increases by one unit. 
D) change in E(y)when x increases by 1%. 
A) change in E(y)when x increases by one unit. 
B) percentage change in E(y)when x increases by 1%. 
C) percentage change in E(y)when x increases by one unit. 
D) change in E(y)when x increases by 1%.

Question 3

Exhibit 16-1.The following Excel scatterplot with the fitted quadratic regression equation illustrates the observed relationship between productivity and the number of hired workers.   Refer to Exhibit 16.1.What is the percentage of variations in the productivity explained by the number of hired workers?

Accepted Answer

A) 85.69% 
B) 0.7342% 
C) 90.54% 
D) 73.42% 
A) 85.69% 
B) 0.7342% 
C) 90.54% 
D) 73.42%

Question 4

How many coefficients have to be estimated in the quadratic regression modely = β0 + β1x + β2x2 + ε?

Accepted Answer

A) 4 
B) 3 
C) 2 
D) 1 
A) 4 
B) 3 
C) 2 
D) 1

Question 5

Exhibit 16.2.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 Excel output illustrates this rather unusual relationship.   Refer to Exhibit 16.2.Using the quadratic equation,predict the sales if the luxury good is priced at $100.

Accepted Answer

A) 1191.87 
B) 1157.64 
C) 1160.79 
D) 1168.00 
A) 1191.87 
B) 1157.64 
C) 1160.79 
D) 1168.00

Question 6

The curve representing the regression equation   has a U-shape if b2 > 0.

Accepted Answer

A) True 
 B)False

Question 7

Exhibit 16.2.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 Excel output illustrates this rather unusual relationship.   Refer to Exhibit 16.2.For which price do sales predicted by the quadratic equation reach their minimum?

Accepted Answer

A) 106.33 
B) 1157.16 
C) 100.41 
D) 1166.64 
A) 106.33 
B) 1157.16 
C) 100.41 
D) 1166.64

Question 8

Exhibit 16-4.The following data shows the cooling temperatures of a freshly brewed cup of coffee after it is poured from the brewing pot into a serving cup.The brewing pot temperature is approximately 180º F;see http://mathbits.com/mathbits/tisection/statistics2/exponential.htm   For the assumed exponential model ln(Temp)= β0 + β1Time + ε,the following Excel regression partial output is available.     Refer to Exhibit 16-4.During one minute,the predicted temperature decreases by approximately

Accepted Answer

A) 0.0118 0F. 
B) 1.18 0F. 
C) 1.18 %. 
D) 11.8 %. 
A) 0.0118 0F. 
B) 1.18 0F. 
C) 1.18 %. 
D) 11.8 %.

Question 9

The fit of the regression equations   and   can be compared using the coefficient of determination R2.

Accepted Answer

A) True 
 B)False

Question 10

Exhibit 16.2.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 Excel output illustrates this rather unusual relationship.   Refer to Exhibit 16.2.Which of the following models is most likely to be chosen in order to describe the relationship between Price and Sales?

Accepted Answer

A) Linear 
B) Quadratic 
C) Cubic 
D) Exponential 
A) Linear 
B) Quadratic 
C) Cubic 
D) Exponential

Question 11

Exhibit 16.6.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.   Refer to Exhibit 16.6.Suppose the restriction β3 = 0 is imposed on the cubic model Debt = β0 + β1Age + β2Age2+ β3Age3 + ε.What regression equation is obtained under this restriction?

Accepted Answer

The quadra

Question 12

The linear and logarithmic models,y = β0 + β1x + ε and y = β0 + β1ln(x)+ ε,were used to 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 13

For the logarithmic model y = β0 + β1ln(x)+ ε,β1/100 is the approximate change in E(y)when x increases by one percent.

Accepted Answer

A) True 
 B)False

Question 14

What does a positive value for price elasticity indicate if y represents the quantity demanded of a particular good and x is its unit price in a log-log regression model?

Accepted Answer

A) As price increases,the expected sales decreases. 
B) As price decreases,the expected sales increases. 
C) As price increases,the expected sales increases. 
D) As price decreases,the expected sales remain the same. 
A) As price increases,the expected sales decreases. 
B) As price decreases,the expected sales increases. 
C) As price increases,the expected sales increases. 
D) As price decreases,the expected sales remain the same.

Question 15

Exhibit 16.6.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.   Refer to Exhibit 16.6.What is the predicted percentage debt of a 45 year old employed single person determined by the model with the best fit?

Accepted Answer

The answer of Exhibit 16.6.Thirty employed single individuals were randomly...

For the model ln(y)= β₀ + β₁ln(x)+ ε with 0 < β₁ < 1,if x increases than E(y)increases but at a slower rate.

In the model ln(y)= β₀ + β₁ln(x)+ ε,the coefficient β₁ is the approximate:

How many coefficients have to be estimated in the quadratic regression modely = β₀ + β₁x + β₂x² + ε?

The curve representing the regression equation has a U-shape if b₂ > 0.

The fit of the regression equations and can be compared using the coefficient of determination R².

The linear and logarithmic models,y = β₀ + β₁x + ε and y = β₀ + β₁ln(x)+ ε,were used to fit given data on y and x,and the following table summarizes the regression results.Which of the two models provides a better fit?

For the logarithmic model y = β₀ + β₁ln(x)+ ε,β₁/100 is the approximate change in E(y)when x increases by one percent.

What does a positive value for price elasticity indicate if y represents the quantity demanded of a particular good and x is its unit price in a log-log regression model?

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Basic Probability Concepts

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

For the model ln(y)= β0 + β1ln(x)+ ε with 0 < β1 < 1,if x increases than E(y)increases but at a slower rate.

In the model ln(y)= β0 + β1ln(x)+ ε,the coefficient β1 is the approximate:

How many coefficients have to be estimated in the quadratic regression modely = β0 + β1x + β2x2 + ε?

The curve representing the regression equation has a U-shape if b2 > 0.

The fit of the regression equations and can be compared using the coefficient of determination R2.

The linear and logarithmic models,y = β0 + β1x + ε and y = β0 + β1ln(x)+ ε,were used to fit given data on y and x,and the following table summarizes the regression results.Which of the two models provides a better fit?

For the logarithmic model y = β0 + β1ln(x)+ ε,β1/100 is the approximate change in E(y)when x increases by one percent.

What does a positive value for price elasticity indicate if y represents the quantity demanded of a particular good and x is its unit price in a log-log regression model?

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Basic Probability Concepts

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

For the model ln(y)= β₀ + β₁ln(x)+ ε with 0 < β₁ < 1,if x increases than E(y)increases but at a slower rate.

In the model ln(y)= β₀ + β₁ln(x)+ ε,the coefficient β₁ is the approximate:

How many coefficients have to be estimated in the quadratic regression modely = β₀ + β₁x + β₂x² + ε?

The curve representing the regression equation has a U-shape if b₂ > 0.

The fit of the regression equations and can be compared using the coefficient of determination R².

The linear and logarithmic models,y = β₀ + β₁x + ε and y = β₀ + β₁ln(x)+ ε,were used to fit given data on y and x,and the following table summarizes the regression results.Which of the two models provides a better fit?

For the logarithmic model y = β₀ + β₁ln(x)+ ε,β₁/100 is the approximate change in E(y)when x increases by one percent.