The following data show the demand for an airline ticket dependent on the price of this ticket. For the assumed cubic and log-log regression models,Demand = β0 + β1Price + β2Price2 + β3Price3 + ε and ln(Demand)= β0 + β1ln(Price)+ ε,the following regression results are available. Which of the following is the percentage of variations in ln(Demand)explained by the log-log regression equation?

A) 98.52% B) 98.50% C) 91.39% D) 97.93% A) 98.52% B) 98.50% C) 91.39% D) 97.93% A

In which of the following models does the slope coefficient b1/100 measure the approximate percentage change in when x increases by 1%?

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 C

In which of the following models does the slope coefficient b1 × 100 measure the approximate percentage change in when x increases by one unit?

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

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?

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

In which of the following models does the slope coefficient b1 measure the change in when x increases by one unit?

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

Exam 16: Regression Models for Nonlinear Relationships

The following data show the demand for an airline ticket dependent on the price of this ticket. For the assumed cubic and log-log regression models,Demand = β₀ + β₁Price + β₂Price²+ β₃Price³+ ε and ln(Demand)= β₀ + β₁ln(Price)+ ε,the following regression results are available. Which of the following is the percentage of variations in ln(Demand)explained by the log-log regression equation?

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(Multiple Choice)

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Question 1

Correct Answer:

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In which of the following models does the slope coefficient b₁/100 measure the approximate percentage change in when x increases by 1%?

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

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

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Question 3

Correct Answer:

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If the restriction β₃ = 0 is imposed on the cubic regression model,we are obtaining the quadratic regression model.

When not all variables are transformed into logarithms the models are called _______ models.

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Question 4

Which of the following regression models is not polynomial?

(Multiple Choice)

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Question 5

In which of the following models does the slope coefficient b₁ × 100 measure the approximate percentage change in when x increases by one unit?

(Multiple Choice)

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Question 6

For the exponential model ln(y)= β₀ + β₁x + ε,β₁ × 100% is the approximate percentage change in E(y)when x increases by 1%.

(True/False)

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Question 7

The following data,with the corresponding Excel scatterplot,show the average growth rate of Weeping Higan cherry trees planted in Washington,DC.At the time of planting,the trees were one year old and were all six feet in height. Which of the following is the predicted height of an eight-year-old cherry tree that was planted as a one-year-old and six-foot-tall tree?

(Multiple Choice)

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Question 8

If the data are available on the response variable y and the explanatory variable x,and the fit of the quadratic regression model y = β₀ + β₁x + β₂x² + ε is to be tested,standard linear regression can be applied on ________.

(Multiple Choice)

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Question 9

The log-log regression model is ________ in the variables.

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Question 10

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?

(Multiple Choice)

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Question 11

The following data,with the corresponding Excel scatterplot,show the average growth rate of Weeping Higan cherry trees planted in Washington,DC.At the time of planting,the trees were one year old and were all six feet in height. Which of the following is the correlation coefficient between Height and ln(Age)?

(Multiple Choice)

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Question 12

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. What is the sample correlation coefficient between Age and Debt?

(Essay)

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Question 13

Many nonlinear regression models can be studied under the linear regression framework using transformation of the response variable and/or the explanatory variables.

(True/False)

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Question 14

Typically,the sales volume declines with an increase of a product's 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. Using the quadratic equation,predict the sales if the luxury good is priced at $100.

(Multiple Choice)

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Question 15

In which of the following models does the slope coefficient b₁ measure the change in when x increases by one unit?

(Multiple Choice)

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Question 16

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?

(Essay)

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Question 17

The following data show the demand for an airline ticket dependent on the price of this ticket. For the assumed cubic and log-log regression models,Demand = β₀ + β₁Price + β₂Price²+ β₃Price³+ ε and ln(Demand)= β₀ + β₁ln(Price)+ ε,the following regression results are available. Assuming that the sample correlation coefficient between Demand and = exp(26.3660 - 3.2577 ln(Price)+ (0.2071)²/2)is 0.956,what is the predicted demand for a price of $250 found by the model with better fit?

(Multiple Choice)

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Question 18

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. What is the number of estimated coefficients of the cubic regression model?

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Question 19

The equation y = β₀ + β₁x + β₂x² + ε is called a cubic regression model.

(True/False)

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Question 20

Showing 1 - 20 of 115

In which of the following models does the slope coefficient b₁/100 measure the approximate percentage change in when x increases by 1%?

When not all variables are transformed into logarithms the models are called _______ models.

Which of the following regression models is not polynomial?

In which of the following models does the slope coefficient b₁ × 100 measure the approximate percentage change in when x increases by one unit?

For the exponential model ln(y)= β₀ + β₁x + ε,β₁ × 100% is the approximate percentage change in E(y)when x increases by 1%.

If the data are available on the response variable y and the explanatory variable x,and the fit of the quadratic regression model y = β₀ + β₁x + β₂x² + ε is to be tested,standard linear regression can be applied on ________.

The log-log regression model is ________ in the variables.

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?

Many nonlinear regression models can be studied under the linear regression framework using transformation of the response variable and/or the explanatory variables.

In which of the following models does the slope coefficient b₁ measure the change in when x increases by one unit?

The equation y = β₀ + β₁x + β₂x² + ε is called a cubic 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

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Exam 16: Regression Models for Nonlinear Relationships

In which of the following models does the slope coefficient b1/100 measure the approximate percentage change in when x increases by 1%?

When not all variables are transformed into logarithms the models are called _______ models.

Which of the following regression models is not polynomial?

In which of the following models does the slope coefficient b1 × 100 measure the approximate percentage change in when x increases by one unit?

For the exponential model ln(y)= β0 + β1x + ε,β1 × 100% is the approximate percentage change in E(y)when x increases by 1%.

If the data are available on the response variable y and the explanatory variable x,and the fit of the quadratic regression model y = β0 + β1x + β2x2 + ε is to be tested,standard linear regression can be applied on ________.

The log-log regression model is ________ in the variables.

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?

Many nonlinear regression models can be studied under the linear regression framework using transformation of the response variable and/or the explanatory variables.

In which of the following models does the slope coefficient b1 measure the change in when x increases by one unit?

The equation y = β0 + β1x + β2x2 + ε is called a cubic 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

In which of the following models does the slope coefficient b₁/100 measure the approximate percentage change in when x increases by 1%?

In which of the following models does the slope coefficient b₁ × 100 measure the approximate percentage change in when x increases by one unit?

For the exponential model ln(y)= β₀ + β₁x + ε,β₁ × 100% is the approximate percentage change in E(y)when x increases by 1%.

If the data are available on the response variable y and the explanatory variable x,and the fit of the quadratic regression model y = β₀ + β₁x + β₂x² + ε is to be tested,standard linear regression can be applied on ________.

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?

In which of the following models does the slope coefficient b₁ measure the change in when x increases by one unit?

The equation y = β₀ + β₁x + β₂x² + ε is called a cubic regression model.