Question 1

The identification problem would not prevent estimation of a demand curve from price and quantity data if, over the time period sampled, the only thing that varied was the
A) technology of production.
B) level of consumer income.
C) price(s) of substitutes and complements.
D) level of advertising expenditures.

Accepted Answer

A

Question 2

The identification problem would prevent estimation of a demand curve from price and quantity data if, over the time period sampled, the only thing that varied was the
A) technology of production.
B) price(s) of raw materials.
C) level of consumer income.
D) rental cost of capital.

Accepted Answer

If only consumer income varied, it would be difficult to distinguish whether changes in quantity demanded were due to changes in price or changes in income, thus preventing accurate estimation of the demand curve.

Question 3

If the t ratio for the slope of a simple linear regression equation is equal to 3.614 and the critical values of the t distribution at the 1 percent and 5 percent levels of significance, respectively, are 3.499 and 2.365, then the slope is
A) not significantly different from zero.
B) significantly different from zero at both the 1 percent and the 5 percent levels.
C) significantly different from zero at the 1 percent level but not at the 5 percent level.
D) significantly different from zero at the 5 percent level but not at the 1 percent level.

Accepted Answer

The t ratio for the slope is 3.614, which is greater than both the critical values at the 1 percent (3.499) and 5 percent (2.365) levels of significance. This means the slope is significantly different from zero at both the 1 percent and 5 percent levels.

Question 4

Application of simple linear regression analysis to the estimation of a demand equation has yielded the following:
Q = 24 - 2P
If the current product price is P = $6 and the quantity sold per time period is Q = 10, then the error (e) for the current time period is equal to
A) 1.
B) -1.
C) 2.
D) -2.

Accepted Answer

The answer of Application of simple linear regression analysis to...

Question 5

If the t ratio for the slope of a simple linear regression equation is equal to 1.614 and the critical values of the t distribution at the 1 percent and 5 percent levels of significance, respectively, are 3.499 and 2.365, then the slope is
A) not significantly different from zero.
B) significantly different from zero at both the 1 percent and the 5 percent levels.
C) significantly different from zero at the 1 percent level but not at the 5 percent level.
D) significantly different from zero at the 5 percent level but not at the 1 percent level.

Accepted Answer

The t ratio for the slope (1.614) is less than both critical values (3.499 at the 1% level and 2.365 at the 5% level), indicating the slope is not significantly different from zero at either level of significance.

Question 6

A multiple regression analysis based on a data set that consists of 30 observations yielded the following estimated equation:
Q = 120 - 1.1P + 3.7I + 0.90A
Where P is price, I is income, and A is advertising. If the coefficient of determination is 0.80, then the adjusted coefficient of determination is
A) 0.84.
B) 0.78.
C) 0.62.
D) 1.04.

Accepted Answer

The adjusted coefficient of determination is calculated to account for the number of predictors in the model relative to the number of observations. It is given by the formula: $ \bar{R}^2 = 1 - [(1 - R^2)(n - 1) / (n - k - 1)] $, where $ R^2 $ is the coefficient of determination, $ n $ is the number of observations, and $ k $ is the number of predictors. Here, $ R^2 = 0.80 $, $ n = 30 $, and $ k = 3 $ (since there are three predictors: P, I, and A). Plugging these values into the formula gives an adjusted $ R^2 $ that is slightly lower than the unadjusted $ R^2 $, which aligns with option B, 0.78, considering the formula tends to lower the $ R^2 $ value to penalize for the number of predictors.

Question 7

A multiple regression analysis based on a data set that consists of 30 observations yielded the following estimated equation:
Q = 120 - 1.1P + 3.7I + 0.09A
Where P is price, I is income, and A is advertising. If the coefficient of determination is 0.80, then the F statistic is
A) 34.67.
B) 29.35.
C) 21.23.
D) 4.67.

Accepted Answer

The F statistic in a regression analysis is calculated using the formula $F = \frac{R^2 / k}{(1 - R^2) / (n - k - 1)}$, where $R^2$ is the coefficient of determination, $k$ is the number of independent variables, and $n$ is the number of observations. Here, $R^2 = 0.80$, $k = 3$ (since there are three independent variables: P, I, and A), and $n = 30$. Plugging these values into the formula gives $F = \frac{0.80 / 3}{(1 - 0.80) / (30 - 3 - 1)} = \frac{0.2667}{0.007692} = 34.67$.

Question 8

A simple linear regression analysis based on a data set that consists of 20 observations yielded the following estimated equation:
Q = 120 - 3.6P
If the coefficient of determination is 0.81, then the correlation coefficient is equal to
A) 0.81.
B) -0.81.
C) -0.90.
D) 0.90.

Accepted Answer

The coefficient of determination (R²) is 0.81, which means the correlation coefficient (r) is the square root of R². Since the slope of the regression equation is negative (-3.6), the correlation coefficient is also negative. Thus, r = -√0.81 = -0.90.

Question 9

A multiple regression analysis based on a data set that consists of 30 observations yielded the following estimated demand equation:
Q = 120 - 1.1P + 0.04I + 0.90A
Where P is price, I is income, and A is advertising. If price is equal to $1,000, income is equal to $20,000, and advertising expenditures are equal to $5,000, then the predicted quantity demanded (Q) is
A) 6,520.
B) 4,320.
C) 8,015.
D) None of these answers is correct.

Accepted Answer

The answer of A multiple regression analysis based on a...

Question 10

A multiple regression analysis based on a data set that consists of 500 observations yielded the following estimated demand equation: Q = 120 - 1.1P + 0.04I + 0.90A - 0.04P_Z Where P is price, I is income, A is advertising, and P_Z is the price of a related good. If the standard errors of the independent variables are 0.25, 0.5, 0.3, and 0.01, respectively, which of the four variables should be dropped from the equation? A) P B) I C) A D) P_Z

Accepted Answer

The variable I (income) should be dropped because its coefficient (0.04) is smaller than twice its standard error (0.5), indicating it is not statistically significant.

Question 11

The F statistic calculated from a multiple regression analysis is equal to 1.96. If the critical values of the F distribution are 2.42 and 3.47 at the 5 percent and 1 percent levels of significance, respectively, then
A) at least one of the slope coefficients is significantly different from zero.
B) none of the slope coefficients is significantly different from zero.
C) all of the slope coefficients are significantly different from zero.
D) no more than 5 percent (1 out of 20) of the slope coefficients are different from zero.

Accepted Answer

The F statistic (1.96) is lower than both critical values (2.42 at the 5% level and 3.47 at the 1% level), indicating that we cannot reject the null hypothesis that all slope coefficients are equal to zero. This means there is not enough evidence to conclude that any of the slope coefficients are significantly different from zero.

Question 12

The F statistic calculated from a multiple regression analysis is equal to 5.96. If the critical values of the F distribution are 2.42 and 3.47 at the 5 percent and 1 percent levels of significance, respectively, then
A) at least one of the slope coefficients is significantly different from zero.
B) none of the slope coefficients is significantly different from zero.
C) all of the slope coefficients are significantly different from zero.
D) no more than 5 percent (1 out of 20) of the slope coefficients are different from zero.

Accepted Answer

The F statistic (5.96) is greater than both critical values (2.42 at the 5% level and 3.47 at the 1% level), indicating that the null hypothesis (that all slope coefficients are zero) can be rejected at both the 5% and 1% levels of significance. This means that at least one of the slope coefficients is significantly different from zero.

Question 13

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 2.00. From this result, it is clear that
A) multicollinearity is present.
B) multicollinearity is absent.
C) autocorrelation is present.
D) autocorrelation is absent.

Accepted Answer

The Durbin-Watson statistic is used to detect the presence of autocorrelation in the residuals from a regression analysis. A value of approximately 2.00 suggests that there is no autocorrelation present.

Question 14

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 1.00. If the lower test value at the 1 percent level is 1.28 and the upper value is 1.51, then
A) there is no evidence of a problem.
B) there is some evidence of a problem, but it is not significant.
C) there is evidence of a significant problem.
D) there is not sufficient information to determine whether or not there is a problem.

Accepted Answer

The Durbin-Watson statistic of 1.00 is below the lower test value of 1.28, indicating evidence of positive autocorrelation in the residuals, which is a significant problem in regression analysis.

Question 15

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 1.00. If the lower test value at the 1 percent level is 1.28 and the upper value is 1.51, then there is evidence that
A) multicollinearity is present.
B) multicollinearity is absent.
C) autocorrelation is present.
D) autocorrelation is absent.

Accepted Answer

The Durbin-Watson statistic tests for the presence of autocorrelation in the residuals from a regression analysis. A value of 1.00 is below the lower test value of 1.28, indicating positive autocorrelation is present in the data.

Question 16

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 1.49. If the lower test value at the 1 percent level is 1.28 and the upper value is 1.51, then
A) there is no evidence of a problem.
B) there is some evidence of a problem, but it is not significant.
C) there is evidence of a significant problem.
D) there is not sufficient information given to determine whether or not there is a problem.

Accepted Answer

The answer of The application of multiple regression analysis to...

Question 17

The application of multiple regression analysis to a data set yields an F statistic that is highly significant and t ratios that are not significant. This is an indication that
A) autocorrelation is present.
B) multicollinearity is present.
C) homoscedasticity is present.
D) heteroscedasticity is present.

Accepted Answer

When the F statistic in a multiple regression analysis is significant, but the t ratios for the individual predictors are not, this often suggests multicollinearity. Multicollinearity occurs when two or more independent variables in the model are highly correlated with each other, making it difficult to assess the individual effect of each variable on the dependent variable.

Question 18

Autocorrelation can be the result of
A) the omission of an important explanatory variable.
B) using cross-sectional data.
C) multicollinearity.
D) All of the above are correct.

Accepted Answer

Autocorrelation often arises from the omission of an important explanatory variable, which can cause the residuals to be correlated over time.

Question 19

The scatter diagram represents a data set and a plot of the simple linear regression equation estimated from the data. The diagram shows evidence of

A) homoscedasticity.
B) heteroscedasticity.
C) positive autocorrelation.
D) negative autocorrelation.

Accepted Answer

The answer of The scatter diagram represents a data set...

Question 20

The scatter diagram represents the error terms from a simple linear regression estimated from time-series data. The error terms are plotted against time. The diagram shows evidence of

A) homoscedasticity.
B) heteroscedasticity.
C) positive autocorrelation.
D) negative autocorrelation.

Accepted Answer

The answer of The scatter diagram represents the error terms...

Quiz 5: Demand Estimation

The identification problem would not prevent estimation of a demand curve from price and quantity data if, over the time period sampled, the only thing that varied was the

The identification problem would prevent estimation of a demand curve from price and quantity data if, over the time period sampled, the only thing that varied was the

If the t ratio for the slope of a simple linear regression equation is equal to 3.614 and the critical values of the t distribution at the 1 percent and 5 percent levels of significance, respectively, are 3.499 and 2.365, then the slope is

Application of simple linear regression analysis to the estimation of a demand equation has yielded the following: Q = 24 - 2P If the current product price is P = $6 and the quantity sold per time period is Q = 10, then the error (e) for the current time period is equal to

If the t ratio for the slope of a simple linear regression equation is equal to 1.614 and the critical values of the t distribution at the 1 percent and 5 percent levels of significance, respectively, are 3.499 and 2.365, then the slope is

A multiple regression analysis based on a data set that consists of 30 observations yielded the following estimated equation: Q = 120 - 1.1P + 3.7I + 0.09A Where P is price, I is income, and A is advertising. If the coefficient of determination is 0.80, then the F statistic is

A simple linear regression analysis based on a data set that consists of 20 observations yielded the following estimated equation: Q = 120 - 3.6P If the coefficient of determination is 0.81, then the correlation coefficient is equal to

The F statistic calculated from a multiple regression analysis is equal to 1.96. If the critical values of the F distribution are 2.42 and 3.47 at the 5 percent and 1 percent levels of significance, respectively, then

The F statistic calculated from a multiple regression analysis is equal to 5.96. If the critical values of the F distribution are 2.42 and 3.47 at the 5 percent and 1 percent levels of significance, respectively, then

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 2.00. From this result, it is clear that

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 1.00. If the lower test value at the 1 percent level is 1.28 and the upper value is 1.51, then

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 1.00. If the lower test value at the 1 percent level is 1.28 and the upper value is 1.51, then there is evidence that

The application of multiple regression analysis to a time-series data set yields a calculated Durbin-Watson statistic that is equal to 1.49. If the lower test value at the 1 percent level is 1.28 and the upper value is 1.51, then

The application of multiple regression analysis to a data set yields an F statistic that is highly significant and t ratios that are not significant. This is an indication that

Autocorrelation can be the result of

The scatter diagram represents a data set and a plot of the simple linear regression equation estimated from the data. The diagram shows evidence of

The scatter diagram represents the error terms from a simple linear regression estimated from time-series data. The error terms are plotted against time. The diagram shows evidence of