Exam 5: Demand Estimation

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lnQt=a+blnPt+clnGDPt\ln Q _ { t } = a + b \ln P _ { t } + c \ln G D P _ { t } One of the advantages of using the following function in estimation is

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Multicollinearity refers to a situation in which two or more of the independent variables in a regression model are highly correlated.

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After estimating the regression using 10 observations, you obtained the following results: Q=50-0.5P+0.6I (15) (0.12)(0.3) Compute the t-statistics for your estimates for price (P) and income (i). Can we reject the null hypothesis at the 5% significance level?

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For a given sample size, the more independent variables are incorporated in a regression model, the more degrees of freedom the relevant t distribution has.

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Your coworker has computed the unexplained and the total variation in Y and asked you to compute the coefficient of determination Unexpl.var.in Y=t=1n(Y^tYˉ)2=380Y = \sum _ { t = 1 } ^ { n } \left( \hat { Y } _ { t } - \bar { Y } \right) ^ { 2 } = 380 Total.var. in Y=t=1n(YtYˉ)2=990Y = \sum _ { t = 1 } ^ { n } \left( Y _ { t } - \bar { Y } \right) ^ { 2 } = 990

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accounts for the degrees of freedom while adjusted does not.

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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

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Using consumer clinics approach, data is obtained from

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A scatter diagram is a graph of a linear function.

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You have found the b estimate to be b^=1.25\hat { b } = 1.25 with standard error sb^=0.5s _ { \hat { b } } = 0.5 . Assuming you had a large sample, compute the confidence interval for the 5% significance level.

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The estimation of consumer demand by questioning a sample of consumers is referred to as the

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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

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

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Fill in the remaining information and compute the estimated value of b. XtXˉYtYˉ(XtXˉ)(XtXˉ)(XtXˉ)2X _ { t } - \bar { X } \quad Y _ { t } - \bar { Y } \quad \left( X _ { t } - \bar { X } \right) \left( X _ { t } - \bar { X } \right) \quad \left( X _ { t } - \bar { X } \right) ^ { 2 } (t) (X) (Y) 1 10 35 2 15 45 3 12 40 4 20 50

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If the absolute value of the t ratio is larger than the t value taken from the table, then the conclusion is that the slope does not differ from zero.

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A market experiment is carried out by providing consumers with a sum of money that must be spent in a simulated store.

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The significance level of a t test on the slope of a simple linear regression equation measures the probability of drawing an incorrect conclusion when the test indicates that X and Y have a significant relationship.

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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

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The log-linear demand function for Beckler's Frozen Pizzas is: lnQX = 4 - 3.80 lnPX + 0.30 lnPY + 0.15 lnS + lnA + 1.50 lnI The number of pizzas sold per week (QX) depends on the price charged for a pizza (PX), the price charged for a competitor's brand of pizza (PY), the percentage of single-parent families (S), monthly advertising expenditures (A) in thousands, and average annual household income (i)in thousands. (i) If PX=$4.00,PY=$3.50,S=40%,A=$5,000P _ { X } = \$ 4.00 , P _ { Y } = \$ 3.50 , S = 40 \% , A = \$ 5,000 , and I=$40,000I = \$ 40,000 , how many pizzas can B eckler'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 percent and to increase advertising expenditures by 10 percent. 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 percent and increases advertising expenditures by 10 percent while Beckler's competitor lowers the price of its pizza by 20 percent, what effect will this have on the number of Beckler's pizzas sold per week?

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The identification problem refers to the difficulties that a researcher encounters when trying to

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