Deck 4: Estimating and Forecasting Demand

Question 1

A regression coefficient measures:

A) the change in the dependent variable due to a unit change in a particular independent variable.
B) the correlation between the dependent and independent variables.
C) the correlation between the explanatory variables.
D) the intercept of the regression line.
E) the value of the predicted variable when the explanatory variables remain unchanged.

Answer 1

A

Question 2

A regression analysis is said to suffer from multicollinearity when:

A) the dependent and independent variables move in the same direction.
B) two or more explanatory variables tend to move together.
C) the degrees of freedom in the regression is equal to zero.
D) the explanatory variables vary independently of one another.
E) the correlation coefficient between the predicted and the explanatory variables is equal to zero.

Answer 2

B

Question 3

Which of the following is true of uncontrolled market data?

A) Uncontrolled market data is more reliable than controlled market data.
B) Uncontrolled market data shows how changes in various economic variables affect the outcomes in a single market.
C) Uncontrolled market data has little information value.
D) Uncontrolled market data reflects changes in multiple factors at the same time.
E) Valid causal predictions must not be based on uncontrolled data.

Answer 3

D

Question 4

Is it always worthwhile gathering more information about customer needs and preferences?

A) Yes, the cost of gathering information is always negligible.
B) Yes, provided that this information is relevant to the firm's decisions.
C) No, a good rule of thumb is not to spend on information more than 2% of what is at stake in the decision.
D) No, the value of additional information must be compared to its additional cost.
E) Yes, gathering more information enables the firm to forecast demand more accurately.

Question 5

A response bias occurs when:

A) responses do not reflect the true preferences and attitudes of respondents.
B) insufficient sample size tends to lower the variability of the responses.
C) the questions do not reflect the true intentions of the surveyor.
D) different versions of the question are targeted to different segments of respondents.
E) the large sample size makes it difficult for the surveyor to reconcile the various responses.

Question 6

Which of the following is the best definition of a controlled market study?

A) A carefully designed study of a market situation.
B) A study of demand and supply in a single market.
C) A study that varies key economic variables in one or more markets to determine the effects of the changes.
D) A study that assumes differences in sales can be accounted for by unmeasured variables.
E) A study that uses a trial and error method to determine probable market outcomes.

Question 7

If the sample variance of a set of observations is 225, its sample standard deviation is equal to _____.

A) 0.225
B) 15
C) 22.5
D) 0.15
E) 2.25

Question 8

Which of the following statements is correct?

A) The sum of squared errors (SSE) embodies the variation in the dependent variable accounted for by the regression equation.
B) The value of the R-squared statistic exceeds unity if the total sum of squares exceeds the sum of squared errors.
C) The value of the R-squared statistic equals zero when all the observations in a data set are equal to the mean observation.
D) The higher the value of the R-squared statistic, the higher is the goodness of fit of a regression equation.
E) The value of the R-squared statistic is insensitive to the number of explanatory variables in a regression equation.

Question 9

In contrast to simple regression, multiple regression considers:

A) several dependent variables rather than one.
B) several independent variables rather than one.
C) more than one dependent and independent variable.
D) multiple equation specifications in order to find the best statistical fit.
E) both times-series data and cross-section data.

Question 10

Calculate the degrees of freedom in a regression equation if the number of observations is 6 and the number of coefficients in the equation is 2.

A) 12
B) 4
C) 8
D) 3
E) 0.33

Question 11

Which of the following is true of the R-squared statistic?

A) It measures the slope of the regression equation.
B) It measures the proportion of the variation of the dependent variable left unexplained by the multiple-regression equation.
C) It measures the total variation in the dependent variable induced by changes in the explanatory variables.
D) It is the standard error of the coefficient associated with an independent variable.
E) It measures the proportion of the variation of the dependent variable explained by the multiple-regression equation.

Question 12

The following table shows the predicted and the actual sales of a firm in the quarters of a year.
Table 4-1
$\begin{array}{l}\begin{array} { | c | c | c | } \hline&\text { Predicted Sales}&\text { Actual Sales }\\ \text { Quarter } & \text { (in dollars) } & \text { (in dollars) } \\\hline 1 & 20 & 19 \\\hline 2 & 22 & 20 \\\hline 3 & 24 & 21 \\\hline 4 & 28 & 26 \\\hline\end{array}\end{array}$

-Calculate the sum of squared errors of the observations from Table 4-1.

A) 20
B) 34
C) 18
D) 22
E) 15

Question 13

Suppose that the "goodness of fit" of an equation is nearly perfect. What is the value of the R2 statistic in this case?

A) Very close to 0
B) Very close to −1
C) Very close to .5
D) Very close to +1
E) Very close to positive infinity

Question 14

If a study examines several different markets at the same time, and compares outcomes with conditions in each market, it is specifically using:

A) time series data.
B) censored data.
C) controlled data.
D) truncated data.
E) cross-sectional data.

Question 15

Computing the F-statistic allows one to:

A) measure the forecasting accuracy of the regression equation.
B) determine which variable contributes the most explanatory power to the regression.
C) measure the degrees of freedom in the regression.
D) predict the increased explanation of any additional variables that might be included.
E) test the overall statistical significance of the regression equation.

Question 16

Which of the following is true of the t-statistic?

A) It is the value of the coefficient estimate divided by its standard error.
B) It is the sum of the value of the coefficient estimate and its standard error.
C) It is the coefficient's standard error normalized to lie between 0 and 1.
D) It measures the overall statistical validity of the regression equation.
E) It tells us how many standard errors the coefficient estimate is equal to zero.

Question 17

Calculate the standard error of a regression equation if the sum of squared errors of the observations is 625 and the degrees of freedom in the regression is 25.

A) 5
B) 10
C) 7.5
D) 2.5
E) 25

Question 18

The standard error of the regression:

A) measures the explanatory power of the regression equation and lies between 0 and 1.
B) measures the explained variation in the dependent variable.
C) measures the unexplained variation in the dependent variable.
D) is equal to the sum of squared errors minus the total sum of squares.
E) is equal to the slope of the regression equation.

Question 19

The difference between the predicted value and the actual value of a variable in a regression analysis is called:

A) absolute divergence.
B) estimation error.
C) standard error.
D) mean deviation.
E) variance.

Question 20

Heteroscedasticity occurs when:

A) the variance of the random error is non-constant over the sample.
B) the regression coefficient estimates are highly unstable.
C) the random errors are correlated over time.
D) two or more explanatory variables are highly correlated.
E) the dependent and the explanatory variables are highly uncorrelated.

Question 21

What are the major advantages and drawbacks of using controlled market studies to estimate demand?

Question 22

What are the four major pitfalls of using consumer surveys to forecast demand?

Question 23

Carefully explain why adjusted R2 is always less than R2.

Question 24

Jim Bradley is the manager of a bakery, located on a major intersection in a suburban area of Midwestern city. He has been collecting data on sales at his store for the past year. Recently, he has developed a model that he thinks explains sales at the bakery. Unfortunately, he never had a course in statistics, and isn't sure that he has done his regression analysis correctly and asks for your opinion.
According to Jim, weekly sales at the Bradley Bakery can be described by the equation:
Q = 5,000 - 1,000P + 10A + 1.5Y + 400P_c - 25A_c, where Q denotes unit sales, P is the firm's price, A is the firm's advertising spending, Y is the per capita income in the local area, P_c is the average price charged by a nearby competing bakery and A_c is the rival's advertising spending. Jim didn't keep the printout from the analysis. He only kept the equation, which he is eager to use to plan for his likely sales in the next few months. What advice would you give Jim about using the equation?

Question 25

You are a newly hired marketing trainee for a local corporation. Senior management has wondered how other local firms view your company's reputation. One suggestion is to call a variety of managers from a master contact list of firms that your firm has done business with over the last 12 months and ask them what they think of the company. How reliable is this kind of survey method?

Question 26

Suppose that in a given regression, the R2 = .945, the number of observations is 14, and the number of coefficients is 5. What is the adjusted R2? (round off your answer up to three decimal places)

Question 27

The equation Q = a + bt represents:

A) an exponential trend.
B) a linear trend.
C) an irregular downward trend.
D) a geometric trend.
E) a quadratic trend.

Question 28

A regression analysis is assumed to be free of serial correlation when the Durbin-Watson statistic for the regression is approximately equal to:

A) -2.
B) 2.
C) 1.
D) -1.
E) 0.

Question 29

How can regression analysis use uncontrolled data to estimate demand?

Question 30

Serial correlation occurs when:

A) the value of the random error in one period depends on one or more independent variables.
B) the random errors are correlated over time.
C) the values of two or more regression coefficients are correlated.
D) two or more independent variables tend to move together.
E) the size of the random error increases over time.

Question 31

Which of the following is true of barometric models?

A) Barometric models accurately predict changes in trends.
B) Barometric models search for patterns among different variables over time.
C) Barometric models determine the magnitude of changes in different variables within a given time frame.
D) Barometric models forecast changes in one variable induced by changes in other variables at a particular point of time.
E) Barometric models explain changes in market outcomes induced by changes in demand or supply.

Question 32

Which of the following can be used to correct for seasonality in time-series modeling?

A) Error terms
B) Binomial coefficients
C) Dummy variables
D) Stochastic constants
E) Confidence intervals

Question 33

An equation's root mean squared error is:

A) a measure of how closely its predictions match actual outcomes.
B) a measure of how closely the equation explains past data.
C) inversely proportional to the difference between the actual value and the predicted value.
D) derived from the R² statistic.
E) equal to the square root of the sum of squared errors.

Question 34

What are the major advantages and drawbacks of using controlled customer experiments to determine demand?

Question 35

Business cycles are:

A) short-term patterns of increases and decreases in economic activity around a general trend.
B) irregular fluctuations in the level of economic activity, which rarely occur anymore.
C) predictable economic expansions above the long-term trend.
D) abrupt and unexpected departures from the current economic trend.
E) periodic fluctuations in aggregate demand that depend on the time of the year.

Question 36

The equation Q = a + bt + ct2 represents:

A) a quadratic trend.
B) a linear trend.
C) a smooth downward trend.
D) a harmonic trend.
E) an exponential trend.

Question 37

What is regression analysis, and what are the major steps in using it?

Question 38

What are the two main categories of forecasting models? How do they differ?

Question 39

An economic variable's trend over time indicates:

A) a general tendency for an event to occur.
B) a steady movement in the variable.
C) an irregular pattern in the movement of an economic variable.
D) a fixed path along which the variable must move.
E) a periodic variation in an economic variable.

Question 40

A time-series model attempts to identify:

A) patterns of changes in a single variable over time.
B) possible links between a dependent variable and a single independent variable over time.
C) possible links between a dependent variable and one or more independent variables over time.
D) the key factors that help predict future economic events.
E) patterns of forecast errors over time.

Question 41

(a) If a forecaster is analyzing sales of gasoline in a large city during the next two years, which time-series component is likely to be most important?

Question 42

What role do leading indicators play in forecasting? What are some of their limitations?

Question 43

Rail Tours, Inc. sells packaged tours on rail lines, including gourmet meals and a reserved bed. The most popular tours are in the autumn, when foliage colors are at their peak. The overnight package for Saturday and Sunday morning are especially heavily booked. A market survey firm has just completed a study in which they conclude that if the package cost is $200 per couple, then Rail Tours can expect to sell 400 spaces on a typical Saturday. If the price is raised to $225, then unit sales will drop to 390. If the price is raised further to $250, unit sales drop to 380.
(a) From the data given, write down the demand equation and determine its intercepts. Are there any precautions needed when operating at the extreme ends of the demand curve?

Question 44

A firm has prepared two different models to be used for forecasting. One has a fairly large root mean squared error (RMSE), the other has a much smaller RMSE. Which forecast would you expect to give the more accurate prediction? Explain.

Question 45

Fred Smith of the Dodge City Bank has received several loan applications from local small businesses. The applications are supported by various documentations, including the business plans of the firms. Each applicant has submitted forecasts of sales and profits for his or her business. Smith must decide which (if any) loans to approve. Because the ability of the firms to pay off the loans depends on the accuracy of the forecasts, he is especially concerned. He has called on you, his newly hired assistant, to help determine the reliability of the forecasts. What do you tell him about these forecasts and their accuracy to help him make his decision?

Question 46

How would a forecaster determine which functional form of an equation to use to predict a variable?

Question 47

Why is identification a problem in demand estimation? What management errors might occur if a demand relationship is not properly identified?

Question 48

Sales at a store are currently $450,000 per year. If sales are predicted to increase by 5% per year, forecast sales for each of the next 4 years.

Question 49

Gold Tracker monitors the price of precious metals and has developed a forecasting model for the sales of gold: Q = 4,000 − 0.01P + 1.5C − 1.25X + 1.0S, where Q = weekly sales of gold (in millions of ounces), P is the price of gold (dollars per ounce), C is the most recent one-month report of the consumer price index of inflation (in percent), X is an index of the exchange rate of the U.S. dollar compared to seven other currencies, and S is the market price of an ounce of silver (dollars per ounce).
(a) Recently, the price of gold has been $380 per ounce, inflation was measured at 0.2% for the month, the dollar has been trading at 99.7 on the foreign exchange index, and silver has been steady at $9.50 per ounce. What is the expected quantity of gold traded per week?

Question 50

Liza is a manager of a leading soft drink manufacturing firm. Liza uses 10 months data and estimates the following demand equation:
Q = 10 - .5P + 1.5Y + .25P_R
(2) (.17) (.75) (.50)
where P is the price of the soft drink manufactured by Liza's firm, Y refers to household per capita income, and P_R is the price of a rival soft drink manufacturing firm. The standard errors of the coefficients are given in the parentheses. Which of the explanatory variables have significant effects on the demand for soft drink manufactured by Liza's firm? Explain.
(At 95% confidence level, the relevant t-statistic for 6 degrees of freedom is 1.94)

Question 51

You have taken over your parents' small dry-cleaning shop, and are interested in forecasting demand for your services. Your parents never quite got around to trying to measure demand, but they have kept extensive price and sales records. Using this data, you employ multiple regression techniques and estimate the following logarithmic equation:
Log(Q) = .95 − .6Log(P) + .9Log(Y) + .25Log(Pc),
where Q is the number of shirts laundered per week, P is the price in dollars of a laundered shirt, Y is the per capita income in the local area, and Pc is the price charged by another dry cleaner two blocks away. The number of observations is 39 (i.e., nine months of weekly data). The equation's R² is 0.85, the standard error of the estimate is 200, and the standard errors for the rightside variables are .45, .15, .39, and .18 respectively.
(a) Interpret the demand equation and discuss the associated regression statistics.

Question 52

What are the different categories into which a time-series pattern can be broken? Briefly describe each.

Question 53

What role does uncertainty play in forecasting? Explain.

Question 54

The Dodge City Bank is planning its loans for the next several years, and is using a model of loan demand developed from past experience. Fred Smith is responsible for developing the mortgage loan component of total loan demand. Fred estimates the following equation using 14 years of data:
Q = 50 − .2P − .2D + .3Y + .15H, R² = 0.844
(17) (.13) (.16) (.08) (.06)
Here, Q denotes mortgage loan demand (in million dollars), P denotes the prime interest rate, D is the discount rate, Y is per capita income (in thousand dollars), and H is an index of average city housing prices (in thousand dollars). The standard error of the regression is 22, and standard errors of the coefficients are shown in parentheses. (At 95% confidence level, the relevant t-statistic is 1.83 for 9 degrees of freedom.)
(a) Fred thinks that the discount rate will be 6% in the next year, the prime rate will be 7.75%, per capita income in Dodge City will be $21,000, and housing prices will be $165,000. How many loans can Dodge City Bank expect to make in the next year?

Question 55

INSITE Corporation produces advanced analytic software for computer simulations called "Model It". Based on a regression analysis of product sales in the first year after launch, INSITE's marketing department estimates the demand for "Model It" to be:
Q_M = 1,200 - 8P_M + 4P_S with adjusted R² = 0.65, and with all of the above coefficients statistically significant. Here, Q_M denotes units sold of "Model It" software, P_M denotes "Model It's" price, and P_S denotes the price of a best-selling statistical software package (with both prices in dollars).
(a) Currently, P_M = $200 and P_S = $300. What is the predicted demand for "Model It" software? The price P_S has been unchanged (at $300) during the last 6 months. Given this information, write down the equation for "Model It's" demand curve (with Q_M as the left-side variable). Also determine its inverse demand curve (with P_M as the left-side variable).

Question 56

What are the major sources of information that can be used to estimate demand? What are the major benefits and drawbacks of each?