Exam 4: Estimating and Forecasting Demand

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

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.

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

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.

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?

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

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? (b) Fully evaluate these regression results, including computation of t-statistics, adjusted R², and the F-statistic. (c) Can there be multicollinearity in this model? If so, how should Fred adjust his forecast for this fact?

A regression coefficient measures:

The following table shows the predicted and the actual sales of a firm in the quarters of a year. Table 4-1 Predicted Sales Actual Sales Quarter (in dollars) (in dollars) 1 20 19 2 22 20 3 24 21 4 28 26 -Calculate the sum of squared errors of the observations from Table 4-1.

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? (b) Forecast sales of gold for the next two weeks if gold’s price is expected to rise by 1% per week, inflation is expected to remain constant, the dollar is expected to fall by 5% per week, and the price of silver is expected to rise by 2% per week.

Business cycles are:

Which of the following statements is correct?

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

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

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. (b) If you were to raise the price per shirt, what would happen to total revenue? (c) Evaluate the impact of the other dry cleaner’s price on your sales. (At the 95% confidence level, the relevant t-statistic is about 2.04 for 35 degrees of freedom). (d) Were your parents maximizing profit? If not, suggest an appropriate course of action to increase profitability

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

The standard error of the regression:

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

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?

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.