Question 1

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

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 2

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.   Using Excel's regression,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:   (Use Excel. )Which of the two models provides a better fit?

Accepted Answer

The estimated linear and log-log regress

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.   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

If in the cubic regression mod

Question 4

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 does the slope of the obtained log-log regression equation   = 26.3660 - 3.2577 ln(Price)signify?

Accepted Answer

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%.

Question 5

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.   Using Excel's regression,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:   What is the percentage of variations in the sales of Pepsi as explained by the estimated linear model?

Accepted Answer

The estimated linear regression model is

Question 6

The cubic regression model,y = β0 + β1x + β2x2 + β3x3 + ε,is used when we assume that the relationship between x and y should be captured by a function that has either minimum or maximum,but not both.

Accepted Answer

A) True 
 B)False

Question 7

The linear and logarithmic models,y = β0 + β1x + ε and y = β0 + β1 ln(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 8

A model with one explanatory variable being the only one transformed into its natural logarithm is called a(n)___________.

Accepted Answer

A)  log-log model 
B)  logarithmic model 
C)  exponential model 
D)  linear model 
A)  log-log model 
B)  logarithmic model 
C)  exponential model 
D)  linear model

Question 9

The following Excel scatterplot with the fitted quadratic regression equation illustrates the observed relationship between productivity and the number of hired workers.   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 10

For the quadratic regression equation   = b0 + b1x + b2x2,the predicted y achieves its optimum (maximum or minimum)when x is _________.

Accepted Answer

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

Question 11

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.   Using Excel's regression,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:   Discuss the choice between the linear model and the log-log model.

Accepted Answer

The estimated linear and log-log regress

Question 12

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.   Using Excel's regression,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 estimated log-log model,interpret the estimated coefficient of ln(Pepsi Price).

Accepted Answer

The estimated log-log regression model i

Question 13

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 14

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.     If the age of a tree increases by 1%,then its predicted height increases by approximately _________.

Accepted Answer

A)  6.1082% 
B)  0.06108% 
C)  6.1082 feet 
D)  0.061082 feet 
A)  6.1082% 
B)  0.06108% 
C)  6.1082 feet 
D)  0.061082 feet

Question 15

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

Accepted Answer

Because the linear,quadratic,and cubic m

Question 16

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.   Using Excel's regression,the linear model Pepsi Sales = β0 + β1Pepsi Price + β2Cola Price + ε and the log-log model ln(Pepsi Sales)= β0 + β1 ln(Pepsi Price)+ β2 ln(Cola Price)+ ε have been estimated as follows:   For the estimated linear model,when the Cola Price is held constant what is the predicted change in the Pepsi Salesif the Pepsi Price increases by 10 cents?

Accepted Answer

The estimated linear regression model is

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.   Using Excel's regression,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 estimated linear model,when the Pepsi Price is held constant what is the predicted change in the Pepsi Salesif the Cola Price increases by 10 cents?

Accepted Answer

The estimated linear regression model is

Question 18

Although a polynomial regression model of order two or more is nonlinear,when it is fitted to the data we use the _______ regression to make this fit.

Accepted Answer

A)  nonlinear 
B)  logistic 
C)  polynomial 
D)  linear 
A)  nonlinear 
B)  logistic 
C)  polynomial 
D)  linear

Question 19

What is the effect of b2 0 + b1x + b2x2?

Accepted Answer

A)  The curve is U-shaped. 
B)  The curve is inverted U-shaped. 
C)  The curve is a straight line. 
D)  The curve is not a parabola. 
A)  The curve is U-shaped. 
B)  The curve is inverted U-shaped. 
C)  The curve is a straight line. 
D)  The curve is not a parabola.

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.   Using Excel's regression,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 the estimated log-log model,calculate the predicted Pepsi Sales when the Pepsi Price is $1.50 and the Cola Price is $1.25.

Accepted Answer

The estimated log-log regression model i

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

The cubic regression model,y = β₀ + β₁x + β₂x² + β₃x³+ ε,is used when we assume that the relationship between x and y should be captured by a function that has either minimum or maximum,but not both.

The linear and logarithmic models,y = β₀ + β₁x + ε and y = β₀ + β₁ ln(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?

A model with one explanatory variable being the only one transformed into its natural logarithm is called a(n)___________.

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

For the quadratic regression equation = b₀ + b₁x + b₂x²,the predicted y achieves its optimum (maximum or minimum)when x is _________.

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?

Although a polynomial regression model of order two or more is nonlinear,when it is fitted to the data we use the _______ regression to make this fit.

What is the effect of b₂ < 0 in the case of the quadratic equation = b₀ + b₁x + b₂x²?

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

The cubic regression model,y = β0 + β1x + β2x2 + β3x3 + ε,is used when we assume that the relationship between x and y should be captured by a function that has either minimum or maximum,but not both.

The linear and logarithmic models,y = β0 + β1x + ε and y = β0 + β1 ln(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?

A model with one explanatory variable being the only one transformed into its natural logarithm is called a(n)___________.

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

For the quadratic regression equation = b0 + b1x + b2x2,the predicted y achieves its optimum (maximum or minimum)when x is _________.

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?

Although a polynomial regression model of order two or more is nonlinear,when it is fitted to the data we use the _______ regression to make this fit.

What is the effect of b2 < 0 in the case of the quadratic equation = b0 + b1x + b2x2?

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 ln(y)= β₀ + β₁ln(x)+ ε,the predicted value of y is computed by _______________.

The cubic regression model,y = β₀ + β₁x + β₂x² + β₃x³+ ε,is used when we assume that the relationship between x and y should be captured by a function that has either minimum or maximum,but not both.

The linear and logarithmic models,y = β₀ + β₁x + ε and y = β₀ + β₁ ln(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 quadratic regression equation = b₀ + b₁x + b₂x²,the predicted y achieves its optimum (maximum or minimum)when x is _________.

What is the effect of b₂ < 0 in the case of the quadratic equation = b₀ + b₁x + b₂x²?