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ESTIMATING AND FORECASTING DEMAND

The following table shows the five topic sections of this chapter and the associated study guide problems that pertain to each topic section.

Section Topic

1 Collecting Data

Problems M1-M4, S1, L1.

2 Regression Analysis

Problems M5-M14, S2-S7, L2-L6.

3 Forecasting

Problems M15-M21, S8-S12, L7-L9.

4 Appendix: Regression Using Spreadsheets

Problems L10-L11.

Multiple Choice

M1 Can a demand equation give useful predictions?

a. Yes, generally with very small margins of error.

b. Yes, once the various statistical sources of error are recognized.

c. No, demand equations explain only past behavior, not future sales.

d. No, because economic uncertainty renders all predictions problematic.

e. Yes, because the firm is able to control the key demand factor, price.

M2 Which of the following is the best definition of sample bias?

a. Survey responants who are biased against the product.

b. Market research that surveys an unrepresentative sample of people.

c. Sampling only a portion of the buying public.

d. Market research that biases answers to suit management.

e. Questions framed so as to unintentionaly bias subject answers.

M3 What method did Coca-Cola use to measure the potential market response to the contemplated launch of New Coke?

a. Detailed questionnaires mailed to the public.

b. Controlled consumer experiments.

c. Surveys of actual buying habits of cola drinkers.

d. Econometric forecasts of cola drinkers’ preferences.

e. Regional test marketing accompanied by promotions.

M4 In a typical market experiment, how reliable are the results over a long period of time?

a. Very reliable in the long run, less so in the short run.

b. Quite reliable in the long run and the short run.

c. Unreliable in both the long run and the short run.

d. Reliable in the short run, less so in the long run.

e. Reliable for as long as a decade.

M5 Regression analysis is a statistical technique that

a. Uncovers regular patterns in irregular-looking economic variables.

b. Allows close comparisons of economic variables.

c. Transforms (or normalizes) key economic variables.

d. Determine the historical patterns of economic variables.

e. Quantifies the dependence of a given economic variable on one or more other variables

M6 If a price-quantity relationship lies exactly on a predicted equation line, the value of the sum of squared errors will be

a. One.

b. 100%.

c. Zero.

d. Negative one.

e. Uncertain. More information is need to provide and exact answer.

M7 If a market researcher uses regression analysis on uncontrolled market data, are the results generally useful in understanding demand?

a. No, uncontrolled data are problematic when it comes to studying markets.

b. No, such data are inappropriate as inputs for regression analysis.

c. Uncertain, depends on the questions in which the researcher is interested.

d. Yes, regression analysis can complement and substitute for controlled market data.

e. Yes, though regression analysis is unable to separate the various economic effects.

M8 In a regression, the R2 Statistic is .875. This means that

a. 87.5% of the variation of the dependent variable is explained by the regression equation.

b. 87.5% of the variation of the independent variable is explained by the regression equation.

c. 12.5% of the variation of the dependent variable is explained by the regression equation.

d. The standard deviation of the dependent variable is .875.

e. The variance of the dependent variable is .875.

M9 In computing the adjusted R², increasing the number of degrees of freedom

a. Increases the value of adjusted R²

b. Leaves the value of adjusted R² unchanged.

c. Decreases the value of adjusted R².

d. Uncertain, it depends on the number of observations in the data.

e. Uncertain, it the number of explanatory variables included in the equation.

M10 The standard error of a regression coefficient measures

a. The overall precision of the regresion equation.

b. The standard deviation of the estimated coefficient.

c. The statistical significance of the estimated coefficient.

d. The inverse of the coefficient’s estimated t-statistic.

e. The variance of the estimated regression coefficient.

M11 In regression analysis, the exact specification of the estimated equation is

a. Unimportant; the researcher can choose any desired form for specification.

b. Unimportant; as long as the researcher chooses a linear form for the specification.

c. Important; the chosen form should make economic and statistical sense.

d. Important; the researcher should always use the form that best fits the data.

e. Unimportant, because the point of regression analysis is to use statistics to develop the equation form and the associated coefficients.

M12 In a regression with a high value of R2, two of five explanatory variables have very low t-values. The best course of action is to

a. Use the equation as is.

b. Estimate a new equation dropping two of the explanatory variables.

c. Drop one of the two explantory variables and see if the remaining four have adequate t-values.

d. Consider alternative equation forms for the regression..

e. Answers b, c, and d are all correct.

M13 A p-value of .03 for the coefficient of an explanatory variable

a. indicates the variable is statistically significant.

b. indicates the variable is not statistically significant.

c. roughly shows that the null hypothesis of a zero coefficient is very unlikely.

d. Answers a and c are both correct.

e. shows that the variable explains 3% of the variation in the dependent variable.

M14 If a key explanatory variable is omitted from a regression equation, this

a. typically worsens the R2 of the equation.

b. biases the coefficients of the included expanatory variables.

c. sometimes leads to better forecasts.

d. Answers a and c are both correct.

e. Answers a and b are both correct.

M15 Time-series patterns can be decomposed into

a. Trends and business cycles.

b. Past fluctuations and future fluctuations.

c. Seasonal variations and random fluctuations.

d. Answers a and c are both correct.

e. Changes caused by economic variables.

M16 An economic variable’s trend over time displays

a. An abrupt change from the past pattern.

b. A constant rate of change over time.

c. A smooth, regular pattern.

d. Predictable cycles upward than downward.

e. None of the answers above is correct.

M17 Random fluctuations occur because of

a. Regularly occurring events, overlooked by decision makers.

b. The interplay of business cycles and seasonal variations.

c. Irregular trends that tend to move against each other.

d. Unpredictable factors.

e. Evolving shifts in supply and demand.

M18 Over a long time period, the most important component in a time series is

a. The trend (average) growth rate.

b. Business cycles.

c. Seasonal variations.

d. Random fluctuations.

e. Speculative bubbles.

M19 An example of an equation for a linear time trend is

a. Q = a + bt + ct2.

b. Q = a + bt.

c. Q = a + bP.

d. Q = mx + b.

e. Q = abt.

M20 If an exponential equation fits a time series better than a linear trend, one would expect

a. The R2 for the linear equation to be greater than the R2 for the exponential trend.

b. The estimated coefficients for the linear equation to have greater t-statistics than those for the exponential equation.

c. The F-statistic for the exponential equation to be greater than the F-statistic for the linear equation.

d. The R2 for the exponential equation to be greater than the R2 for the linear equation.

e. Answers c and d are both correct.

M21 A barometric model

a. Is a reliable predictor of cause-and-effect relationships.

b. Predicts changes in trends.

c. Makes forecasts based upon patterns in variables over time.

Explains the size of movements of economic variables.

All of the answers above are correct.

M22 Leading indicators are limited because

a. They provide forecasts only for very short time periods.

b. The time between a change in the indicator and the change in a forecast series is rarely consistent.

c. The change in the indicator says little about the magnitude of the change in the forecast series.

d. Answers b and c are both correct.

e. They rely on only one or two indicators (economic variables)

M23 An equation’s average absolute forecasting error

a. Measures how closely an equation fits past data.

b. Normally becomes smaller for forecasts farther in the future.

c. Measures how closely its predictions match actual outcomes.

d. Is able to statistically erase the impact of random fluctuations.

e. All of the answers above are correct.

Short Problems and Questions

S1 What is a controlled market study, and how can it be used to estimate demand?

S2 What does R² measure? How is this statistic used in regression analysis?

S3 In a regression, R² = .744, the number of observations is 19, and the number of coefficients is 6. Compute the F-statistic. Is it significant at the 95% level?

S4 Suppose that regression analysis yields an F-statistic that is almost, but not quite, significant at the 95% level. Does this mean that the information contained in the regression has no value to a manager?

S5 Suppose that the coefficient for a variable is 1.22, and the standard error for the variable is .58. There are 20 observations, and a total of 6 coefficients. Is this particular variable significantly different from zero?

S6 A researcher thinks that a relationship might be curved rather than linear. Suggest two functional forms of the regression equation that could capture such a relationship.

S7 Carefully define simultaneity, and describe how it affects the problem of equation identification.

S8 Explain how a structural model differs from a nonstructural model.

S9 What are the major categories into which a time-series is decomposed? Why are these categories important to managers?

S10 Give an example of an economic variable that is likely to grow at a constant rate, and one that is likely to grow at an exponential rate.

S11 If a leading indicator is sometimes inaccurate, is it of value to a forecaster? Explain.

S12 Describe three factors that limit forecast accuracy.

Longer Problems and Discussion Questions

L1 You are a consultant to a small commuter airline serving several cities in the mountain and western states. The airline provides connecting service to the several major airports in the region, so that customers can fly on to another destination. The airline uses yield management in pricing flights, and has been raising rates for business customers, while dropping rates slightly for pleasure travelers. Profits have improved.

A recent survey, conducted informally by collecting cards submitted by passengers at the end of flights, has revealed general satisfaction with the nature and quality of service, but some discontent among business travelers about the rising price of travel. They are well aware of the cost of travel to their companies. In addition, there have been stories in the business press about the high price of travel for the businesses in the region.

The airline’s marketing department completed a study and a forecast of sales in the next five years. The study concluded that sales are likely to rise with the increase in income and population in the area, and that business sales are most likely to increase over the next five years. Because demand elasticity is fairly low (measured as – 1.4), marketing suggests that further fare increases are likely to improve profits.

Management would like your professional opinion about the reliability of the results. Based on your knowledge of the airline business, what is your prediction about future demand for airline seats from business travelers? What are the likely competitors that the airline will face? What will most likely happen to demand elasticity for airline seats? Explain.

L2 General Steel produces steel products for use in the construction industry. The firm has enjoyed increasing sales in the past several years, and management is interested in

forecasting future sales. The present production and distribution facilities are near capacity, and GS has decided to expand capacity to prepare for future growth. You have been retained as a consultant to help GS choose the optimal plant size for future needs.

The marketing department of GS has produced the following regression analysis of sales (from the past 12 years):

Qt = 375 – 10Pt + 250Yt, + .40Ht + 7.5PCt, R² = .82

(160) (1.7) (80) (.18) (3.85)

where Qt = total sales (in thousands of dollars) in year t; Pt = an index of GS product

prices; Yt, = GDP (in trillions of dollars); Ht = housing starts (in thousands); and PCt = an index of prices charged by United Steel, a close competitor. Standard errors for the coefficients are shown in parentheses. The standard error of the regression is 190.

a. Evaluate and interpret the regression results above. Comment on R², adjusted R², the F-statistic (compute this), and the standard error of the regression.

b. Suppose that Y = $13.2 trillion, H = 900 thousand, and PC = 120. Derive the demand curve for GS.

c. Will a recession significantly affect sales of GS’s product?

d. Is it likely that there is multicollinearity in this regression. Explain.

Is United Steel a close competitor of General Steel? Explain.

L3 An administrative vice president at a Midwestern college has estimated the following equation describing enrollment at his school:

Q = 15,400 – .2T +.lY

where Q = enrollment, T = yearly tuition (in dollars), and Y = average household income in the state (in dollars). He has used 12 years of data to generate his results.

a. Comment on the suitability and usefulness of this regression equation.

Suppose the R² is .616. What is the adjusted R²? What is the F-statistic? Is the regression equation significant with 95% confidence?

c. Assume that income per household is $46,000. If tuition is currently $25,000 per student, what is the price elasticity od demand? Is the school maximizing profit? Explain.

L4 A student in an MBA program has studied a local manufacturing company as a class project. She has analyzed quarterly sales for the past six years. Regression results on sales have resulted in the following specification:

logQ = 2 – 1.25logP + 1.5logY + 0.67logS R² =.611

(.91) (.55) (.84) (.36)

where Q = unit sales, P = price in dollars, Y = an index of regional income, and S = the price charged by a rival firm. Standard errors are in parentheses.

a. Rewrite this equation to transform it out of the log-log form.

b. Determine which (if any) of the variables are significant determinants of sales. Is the equation as a whole significant?

c. Suppose that P = $15, Y = 102, and S = $12.50. Determine the firm’s predicted sales.

d. Is demand elastic? Explain.

L5 A recent study by an industry trade association on light truck demand has posited the following equation form:

Q = aPbYcFd,

where Q = light truck registrations in a calendar year, P = real price index for light trucks, Y = real per capita disposable income, and F = real price of a gallon of fuel for light trucks.

a. Rewrite the equation in a form that can be estimated with regression analysis.

b. What are the expected signs of coefficients b, c, and d as implied by economic theory?

c. The study has estimated the equation using a time series of data for 10 years. Suppose that the R² statistic is .49. Is the regression meaningful in explaining demand for light trucks? Explain.

L6 What role do omitted variables play in demand estimation?

L7 Peter Van is vice president for financial affairs at Midwest College, and has been working on the student enrollment forecast for the upcoming academic year. He believes that next year’s enrollment is largely based on the current enrollment at Midwest, but is not sure about how to express the relationship.

a. Write an equation for next year’s enrollment, assuming that it depends linearly on this year’s enrollment.

b. Van thinks that enrollment grows by a constant absolute amount every year. Write down the appropriate predictive equation.

c. Suppose instead that Van thinks enrollment grows by 2% a year. Formulate the new forecasting equation.

d. You are an economics major, working in Van’s office on a work-study basis to help pay your tuition. Suggest at least two improvements (based on economic theory) that might help in predicting next year’s enrollment.

L8 Let’s reconsider the estimated regression equation in problem L4:

logQ = 2 – 1.25logP + 1.5logY + 0.67logS

where Q = unit sales in thousands, P = price in dollars, Y = an index of regional income, and S = the price charged by a competing firm.

Confirm that the equation can be rewritten in the form:

Q = 7.39P-1.25Y1.5S.67,

after noting that antilog(2) = 7.39.

Currently, P = $15, Y = 102, and S = $12.50. Now provide sales forecasts for the next four quarters if P is held constant, Y rises by 1% each quarter, and S rises by 2% each quarter.

c. Discuss the importance of sensitivity analysis in relation to these forecasts.

L9 For a 9-year period, real housing prices (after adjusting for inflation) in a region have averaged 8% annual growth. Write down the time trend equation that best fits this 9-year experience. How should one go about forecasting housing prices for the next 5 years? .

L10 A firm that produces a unique product has collected data (listed in the accompanying table) on price and quantity sold in each month during the past year. Price changes have been due to changes in the firm’s production costs. It is believed that market demand has been stable over this time period.

Month Quantity Price

Jan 1,500 12

Feb 1,900 10

Mar 1,800 12

Apr 2,600 7

May 2,400 8

Jun 1,150 14

Jul 900 16

Aug 1,200 14

Sep 1,700 11

Oct 2,000 10

Nov 2,300 9

Dec 1,800 10

a. What is the mean and standard deviation of quantity?

b. What is the mean and standard deviation of price?

c. Estimate the firm’s linear demand curve in the form: Q = a + bP using ordinary least squares regression.

d. Estimate the firm’s demand curve in the form: Q = aPb using ordinary least squares regression.

L11 A tool producer has collected data on price and quantity sold for a particular hand-tool over the past ten years. The firm has also collected data on the average price charged by competitors and the percentage rate of growth in consumer income.

a. Estimate the firm’s linear demand curve using ordinary least squares regression.

b. Evaluate the overall quality of the estimation results.

c. Evaluate the significance of each variable in the estimated equation.

Year Quantity Price Rival’s Price Income Growth

1 1,000 6 5 ‑1

2 4,000 5 5 3

3 2,000 6 5 1

4 5,000 3.5 3.5 0

5 5,000 4 4.5 2

6 4,000 7 8 1

7 7,000 8 9 4

8 1,000 7 6 0

9 5,000 5.5 6 3

10 8,000 5 6 4

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