Question 1

regression equation is equal to 3.614 and the critical values of the t distribution at the 1% and 5% 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% and the 5% levels.
C) significantly different from zero at the 1% level but not at the 5% level.
D) significantly different from zero at the 5% level but not at the 1% level.

Accepted Answer

The regression equation's t-value of 3.614 exceeds both critical values (3.499 at the 1% level and 2.365 at the 5% level), indicating the slope is significantly different from zero at both the 1% and 5% levels of significance.

Question 2

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% and 5% 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% and the 5% levels.
C) significantly different from zero at the 1% level but not at the 5% level.
D) significantly different from zero at the 5% level but not at the 1% level.

Accepted Answer

The t ratio for the slope 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 3

If the t ratio for the slope of a simple coefficient of a simple linear regression equation is -2.48 and the critical values of the t distribution at the 1% and 5% levels, 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% and the 5% levels.
C) significantly different from zero at the 1% level but not at the 5% level.
D) significantly different from zero at the 5% level but not at the 1% level.

Accepted Answer

The t ratio for the slope is -2.48, which is less than the critical value at the 1% level (3.499) but greater than the critical value at the 5% level (2.365). Therefore, the slope is significantly different from zero at the 5% level but not at the 1% level.

Question 4

Ordinary least squares is used to estimate a linear relationship between a firm's quantity sold per month and its total promotional expenditures, and the slope of the linear function is found to be positive and significantly different from zero. Assuming that all other variables, including product price, were constant during the period covered by the data set, this result implies that
A) the firm should spend more on promotional expenditures.
B) the firm should spend less on promotional expenditures.
C) promotional expenditures influence demand.
D) promotional expenditures have no influence on demand.

Accepted Answer

A positive and significantly different from zero slope in the context of a linear relationship between a firm's quantity sold per month and its total promotional expenditures, assuming all other variables are constant, implies that there is a positive relationship between promotional expenditures and quantity sold. This means that as promotional expenditures increase, the quantity sold also increases, indicating that promotional expenditures influence demand.

Question 5

Ordinary least squares is used to estimate a linear relationship between a firm's total revenue per week (in $1,000s) and the average percentage discount from list price allowed to customers by salespersons. A 95% confidence interval on the slope is calculated from the regression output. The interval ranges from 1.05 to 2.38. Based on this result, the researcher
A) can conclude that the slope is significantly different from zero at the 5% level of significance.
B) can be 95% confident that the effect of a 1% increase in the average price discount will increase weekly total revenue by between $1,050 and $2,380.
C) has one chance in twenty of incorrectly concluding that the slope is within the estimated confidence interval.
D) All of the above are correct.

Accepted Answer

The confidence interval does not include zero, so the slope is significantly different from zero at the 5% level of significance. The interval also provides a 95% confidence interval for the effect of a 1% increase in the average price discount on weekly total revenue. Finally, the researcher has one chance in twenty of incorrectly concluding that the slope is within the estimated confidence interval.

Question 6

The adjusted value of the coefficient of determination
A) will always increase if additional independent variables are added to the regression model.
B) is equal to the proportion of the sum of the squared deviations of the dependent variable from its mean that is explained by the regression model.
C) is always greater than the proportion of the sum of the squared deviations of the dependent variable from its mean that is explained by the regression model.
D) is always less than the proportion of the sum of the squared deviations of the dependent variable from its mean that is explained by the regression model.

Accepted Answer

The answer of The adjusted value of the coefficient of...

Question 7

The Durbin-Watson statistic is used to test the significance of the standard error of the regression.

Accepted Answer

The Durbin-Watson statistic is used to detect the presence of autocorrelation in the residuals from a regression analysis.

Question 8

If the observed values of the dependent and independent variables are transformed into their natural logarithms, then each estimated slope coefficient is equal to the elasticity of the dependent variable with respect to the corresponding independent variable.

Accepted Answer

When both dependent and independent variables in a regression model are transformed into their natural logarithms, the estimated slope coefficients directly represent the elasticity of the dependent variable with respect to the independent variables. This is because elasticity measures the percentage change in the dependent variable resulting from a one percent change in an independent variable, which is exactly what the logarithmic transformation captures.

Question 9

Just The Fax, Inc. (JTF) has hired you as a consultant to analyze the demand for its line of telecommunications devices in 35 different market areas. The available data set includes observations on the number of thousands of units sold by JTF per month (Q_X), the price per unit charged by JTF (P_X), the average unit price of competing brands (P_Z), monthly advertising expenditures by JTF (A), and average gross sales (in $1,000) of businesses in the market area (I). The results of a regression analysis (with standard errors in parenthesis) are given below. (i) Evaluate the statistical significance of the equation as a whole and of each of its coefficients. (ii) The average values of the independent variables in the data set used to estimate the equation are P_X = $195, P_Z = $225, A = $11,000, and I = $200,000. Calculate a point estimate of JTF's average sales and a 95% interval estimate of sales based on these values.

Accepted Answer

The answer of Just The Fax, Inc. (JTF) has hired...

Question 10

The Drag Net Fishing Company (DNF) has hired you as a consultant to analyze the demand by local restaurants for fresh fish. The available data set includes monthly observations collected over the past five years on the number of hundreds of pounds of fish purchased by local restaurants per month (Q), the price per pound of fish (P), the average cost of a meal at a local restaurant (M), a seasonal variable (S) that is equal to one during the tourist season and zero otherwise, and average household income (in $1,000) in the area. The results of a regression analysis (with standard errors in parenthesis) are given below.
  (i) Evaluate the statistical significance of the equation as a whole and of each of its coefficients.
(ii) The average values of independent variables in the data set that was used to estimate the equation are P = $8, M = $14, and I = $40,000. Calculate a point estimate of the restaurant demand for fish and a 95% interval estimate when it is tourist season. Also, calculate a point estimate of the restaurant demand for fish and a 95% interval estimate when it is not tourist season.

Accepted Answer

The answer of The Drag Net Fishing Company (DNF) has...

Question 11

Florid Technologies is a manufacturer of exercise machines. Their best selling device, a mechanical swimming simulator, has been on the market for several years. The demand function for the simulator was estimated in log-linear form using time-series data. The results are presented below. Q_X = 110 P_X^-0.20 P_Y^0.30 P_Z^-0.10 A^0.10 I^0.01 The number of simulators sold per week (Q_X) was found to depend on the price charged for a simulator (P_X), the average monthly cost of membership at a health club (P_Y), the cost of an accessory package designed for use with the simulator (P_Z), monthly advertising expenditures (A) in thousands, and average annual household income (I) in thousands. (i) If P_X = $595, P_Y = $45, P_Z = $99.85, A = $11,000, and I = $44,000, how many simulators can Florid Industries expect to sell in a week? (ii) Interpret the price elasticity, cross-price elasticities, advertising elasticity, and income elasticity of demand for simulators. (iii) The president of Florid Technologies plans to increase the simulator's price by 10% and to increase advertising expenditures by 5%. By what percentage can sales of simulators be expected to change? Will total revenue increase, decrease, or remain the same? Explain your answer. (iv) If the price of a simulator is increased by 10% and the cost of an accessory package is reduced by 20%, what effect will this have on simulator sales?

Accepted Answer

The answer of Florid Technologies is a manufacturer of exercise...

Question 12

The log-linear demand function for Beckler's Frozen Pizzas is: lnQ_X = 4 - 3.80 ln P_X + 0.30 ln P_Y + 0.15 ln S + ln A + 1.50 ln I The number of pizzas sold per week (Q_X) depends on the price charged for a pizza (P_X), the price charged for a competitor's brand of pizza (P_Y), the percentage of single parent families (S), monthly advertising expenditures (A) in thousands, and average annual household income (I) in thousands. (i) If P_X = $4.00, P_Y = $3.50, S = 40%, A = $5,000, and I = $40,000, how many pizzas can Beckler's expect to sell in a week? (ii) Interpret the price elasticity, cross-price elasticity, family structure elasticity, advertising elasticity, and income elasticity of demand for pizzas. (iii) The president of Beckler's plans to increase the price of their pizzas by 25% and to increase advertising expenditures by 10%. By what percentage can the number of pizzas sold by Beckler's be expected to change? Will total revenue increase, decrease, or remain the same? Explain your answer. (iv) If Beckler's lowers the price of its pizzas by 5% and increases advertising expenditures by 10% while Beckler's competitor lowers the price of its pizza by 20%, what effect will this have on the number of Beckler's pizzas sold per week?

Accepted Answer

The answer of The log-linear demand function for Beckler's Frozen...

Quiz 3: Demand Estimation

regression equation is equal to 3.614 and the critical values of the t distribution at the 1% and 5% levels of significance, respectively, are 3.499 and 2.365, then the slope is

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% and 5% levels of significance, respectively, are 3.499 and 2.365, then the slope is

If the t ratio for the slope of a simple coefficient of a simple linear regression equation is -2.48 and the critical values of the t distribution at the 1% and 5% levels, respectively, are 3.499 and 2.365, then the slope is

The adjusted value of the coefficient of determination

The Durbin-Watson statistic is used to test the significance of the standard error of the regression.

If the observed values of the dependent and independent variables are transformed into their natural logarithms, then each estimated slope coefficient is equal to the elasticity of the dependent variable with respect to the corresponding independent variable.