Exhibit 16.5.The following data shows 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: Refer to Exhibit 16.5.What does the slope of the obtained regression equation signify?

A) For every 1% increase in the price,the predicted demand declines by approximately 3.2577%. B) For every 1% increase in the demand,the expected price increases by approximately 3.2577%. C) For every 1% increase in the demand,the expected price decreases by approximately 3.2577%. D) For every 1% increase in the price,the predicted demand increases by approximately 3.2577%. A) For every 1% increase in the price,the predicted demand declines by approximately 3.2577%. B) For every 1% increase in the demand,the expected price increases by approximately 3.2577%. C) For every 1% increase in the demand,the expected price decreases by approximately 3.2577%. D) For every 1% increase in the price,the predicted demand increases by approximately 3.2577%.

Exam 16: Regression Models for Nonlinear Relationships

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

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Question 1

Correct Answer:

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True

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.What is the percentage of variations in ln(Temp)explained by Time?

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(Multiple Choice)

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Question 2

Correct Answer:

Verified

For the logarithmic model y = β₀ + β₁ln(x)+ ε,the predicted value of y is computed by:

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(Multiple Choice)

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Question 3

Correct Answer:

Verified

The fit of the models y = β₀ + β₁x + ε and y = β₀ + β₁ln(x)+ ε can be compared using the coefficient of determination R².

(True/False)

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Question 4

Given the data on y and x,what is needed to run Excel regression for the polynomial model of order 3?

(Multiple Choice)

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Question 5

The log-log and exponential models,ln(y)= β₀ + β₁ln(x)+ ε and ln(y)= β₀ + β₁x + 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?

(Multiple Choice)

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Question 6

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 estimate of the variance of the random error ε provided by the regression equation with the best fit?

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Question 7

Exhibit 16-7.It is believed that the sales volume of one liter Pepsi bottles depends on the price of the bottle and the price of one liter bottle of Coca Cola.The following data has been collected for a certain sales region. Using Excel's regression,the linear model PepsiSales = β₀ + β₁PepsiPrice + β₂ColaPrice + ε and the log-log model ln(PepsiSales)= β₀ + β₁ln(PepsiPrice)+ β₂ln(ColaPrice)+ ε have been estimated as follows: (Use Excel. )Refer to Exhibit 16.7.Which of the two models provides a better fit?

(Short Answer)

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Question 8

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 value of the test statistic for testing H₀: β₂ = β₃ = 0 against H_A: β₂ ≠ 0 or β₃ ≠ 0 in the model Debt = β₀ + β₁Age + β₂Age²+ β₃Age³ + ε?

(Short Answer)

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Question 9

Exhibit 16-7.It is believed that the sales volume of one liter Pepsi bottles depends on the price of the bottle and the price of one liter bottle of Coca Cola.The following data has been collected for a certain sales region. Using Excel's regression,the linear model PepsiSales = β₀ + β₁PepsiPrice + β₂ColaPrice + ε and the log-log model ln(PepsiSales)= β₀ + β₁ln(PepsiPrice)+ β₂ln(ColaPrice)+ ε have been estimated as follows: Refer to Exhibit 16.7.Using the estimated log-log model,calculate the predicted sales of Pepsi when the Pepsi price is $1.50 and the Cola price is $1.25.

(Short Answer)

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Question 10

Exhibit 16.5.The following data shows 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: Refer to Exhibit 16.5.What does the slope of the obtained regression equation signify?

(Multiple Choice)

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Question 11

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

(True/False)

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Question 12

Exhibit 16-7.It is believed that the sales volume of one liter Pepsi bottles depends on the price of the bottle and the price of one liter bottle of Coca Cola.The following data has been collected for a certain sales region. Using Excel's regression,the linear model PepsiSales = β₀ + β₁PepsiPrice + β₂ColaPrice + ε and the log-log model ln(PepsiSales)= β₀ + β₁ln(PepsiPrice)+ β₂ln(ColaPrice)+ ε have been estimated as follows: (Use Excel. )Refer to Exhibit 16.7.What is the percentage of variations in the sales of Pepsi explained by the estimated log-log model?

(Short Answer)

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Question 13

A model in which the response variable is transformed into its natural logarithm is called a(n)_____.

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Question 14

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.For which value of Hires the predicted Productivity is maximized (Do not round to the nearest integer. )?

(Multiple Choice)

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Question 15

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.Assuming that the number of hired workers must be integer,what is the maximum productivity to achieve?

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Question 16

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.The quadratic regression equation found is:

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Question 17

Exhibit 16-7.It is believed that the sales volume of one liter Pepsi bottles depends on the price of the bottle and the price of one liter bottle of Coca Cola.The following data has been collected for a certain sales region. Using Excel's regression,the linear model PepsiSales = β₀ + β₁PepsiPrice + β₂ColaPrice + ε and the log-log model ln(PepsiSales)= β₀ + β₁ln(PepsiPrice)+ β₂ln(ColaPrice)+ ε have been estimated as follows: Refer to Exhibit 16.7.What is the estimated log-log regression model?

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Question 18

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 percentage of variations in Debt explained by Age in the regression equation with the best fit?

(Short Answer)

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Question 19

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 cubic regression equation,predict the sales if the luxury good is priced at $100.

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Question 20

Showing 1 - 20 of 95

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

For the logarithmic model y = β₀ + β₁ln(x)+ ε,the predicted value of y is computed by:

The fit of the models y = β₀ + β₁x + ε and y = β₀ + β₁ln(x)+ ε can be compared using the coefficient of determination R².

Given the data on y and x,what is needed to run Excel regression for the polynomial model of order 3?

The log-log and exponential models,ln(y)= β₀ + β₁ln(x)+ ε and ln(y)= β₀ + β₁x + 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?

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

A model in which the response variable is transformed into its natural logarithm is called a(n)_____.

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.The quadratic regression equation found is:

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

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

For the logarithmic model y = β0 + β1ln(x)+ ε,the predicted value of y is computed by:

The fit of the models y = β0 + β1x + ε and y = β0 + β1ln(x)+ ε can be compared using the coefficient of determination R2.

Given the data on y and x,what is needed to run Excel regression for the polynomial model of order 3?

The log-log and exponential models,ln(y)= β0 + β1ln(x)+ ε and ln(y)= β0 + β1x + 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?

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

A model in which the response variable is transformed into its natural logarithm is called a(n)_____.

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.The quadratic regression equation found is:

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 logarithmic model y = β₀ + β₁ln(x)+ ε,the predicted value of y is computed by:

The fit of the models y = β₀ + β₁x + ε and y = β₀ + β₁ln(x)+ ε can be compared using the coefficient of determination R².

The log-log and exponential models,ln(y)= β₀ + β₁ln(x)+ ε and ln(y)= β₀ + β₁x + 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?

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