Quiz 5: Demand Estimation and Forecasting
Business
Q 1Q 1
One of the most difficult tasks in regression analysis is to obtain the data suitable for quantitative studies of this kind. Suppose you are trying to estimate the demand for home furniture. Suggest the kinds of variables that could be used to represent the following factors, which are believed to affect the demand for any product. Be as specific as possible about how the variables are going to be measured. Do you anticipate any difficulty in securing such data Explain.
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Regression analysis estimates the relationship between the one dependent variable and one or more independent variable. This means, regression analysis studies the relationship between variables either positively or negatively.
Regression equation is as follows:
Here,
In the problem, determinants of demand for furniture are given as follow:
Regression equation is as follows:
How these determinants determined the demand for furniture
• Price of the furniture: there is an inverse relationship between price of the furniture and demand for furniture.
• Tastes and preferences: there is a positive relationship between tastes and preferences and demand for the product.
• Price of related goods: if the goods are substitutes, there is a positive relationship between the price of one commodity and demand for another commodity.
• Income of the consumer: there is positive relationship between income of the consumer and demand for furniture, because furniture is a luxury good.
• Cost of availability of credit: there is an inverse relationship between cost of the product and demand for furniture.
• Number of consumer: there is a positive relationship between number of buyers and demand for furniture.
• Future expectations: there is a positive relationship between prices of future expectation for the furniture and demand for furniture.
Thus, a change in independent variable will affect the dependent variable either positively or negatively.
Q 2Q 2
If the sales of your company have grown from $500,000 five years ago to $1,050,150 this year, what is the compound growth rate If you expect your sales to grow at a rate of 10 percent for the next five years, what should they be five years from now
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The sales for the company have grown from $500,000 five years ago to $1,050,150 this year. The compound growth rate can be calculated by using the following formula:
……(1)
Where, E = Last year's amount; B = First years amount; I = Growth rate; and n = Number of years.
Substituting the values in equation (1) we get:
So, the compounded growth rate is 16%.
If we expect your sales to grow at a rate of 10 percent for the next five years, than the sales after five years from now can be calculated as follows:
Therefore, sales after 5 years would be $1,691,277.
Q 3Q 3
You are the manager of a large automobile dealership who wants to learn more about the effectiveness of various discounts offered to customers over the past 14 months. Following are the average negotiated prices for each month and the quantities sold of a basic model (adjusted for various options) over this period of time.
a. Graph this information on a scatter plot. Estimate the demand equation. What do the regression results indicate about the desirability of discounting the price Explain.
b. What other factors besides price might be included in this equation Do you foresee any difficulty in obtaining these additional data or incorporating them in the regression analysis
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(a)
The scatter diagram based on the 14 month data related to price and quantity sold of a basic automobile model is given below:
The demand equation for the given set of data can be calculated by using MS-Excel. The equation is given below:
…… (1)
Where Q is the quantity demand and P is the Price.
The regression model suggests that there is a negative relationship between price and quantity sold. If the discount is increase than the sales of the automobile is likely to increase. So, discounting is desirable as per the data available.
(b)
The demand of automobile will depend on a number of other factors which need to be considered in the regression model. The other factors are income of the consumer, price of other automobile models, price of fuel, taste and preference, future expectation.
It will be difficult to finding an exact variable that can be used to measure taste and preference. The other factors can be measured relatively easily and can be used in the regression model.
Q 4Q 4
The sales data for the Lonestar Sports Apparel Company for the last 12 years are as follows:
a. What is the 2001-2012 compound growth rate
b. Using the result obtained in part a, what is your 2013 projection
c. If you were to make your own projection, what would you forecast
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Q 5Q 5
The maker of a leading brand of low-calorie microwavable food estimated the following demand equation for its product using data from 26 supermarkets around the country for the month of April:
Q = -5,200 - 42 P + 20 P X + 5.2 l + 0.20 A + 0.25 M
(2.002) (17.5) (6.2) (2.5) (0.09) (0.21)
R 2 = 0.55 n = 26 F = 4.88
Assume the following values for the independent variables:
Q = Quantity sold per month
P (in cents) = Price of the product = 500
P X (in cents) = Price of leading competitor's product = 600
I (in dollars) = Per capita income of the standard metropolitan statistical area (SMSA) in which the supermarket is located = 5,500
A (in dollars) = Monthly advertising expenditure = 10,000
M = Number of microwave ovens sold in the SMSA in which the supermarket is located = 5,000
Using this information, answer the following questions:
a. Compute elasticities for each variable.
b. How concerned do you think this company would be about the impact of a recession on its sales Explain.
c. Do you think that this firm should cut its price to increase its market share Explain.
d. What proportion of the variation in sales is explained by the independent variables in the equations How confident are you about this answer Explain.
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Q 6Q 6
Based on past data, Mack's Pool Supply has constructed the following equation for the sales of its house brand of chlorine tablets:
Q = 1,000 + 100 t
where Q is quantity and t is time (in years), with 2007 = 0.
a. What is the sales projection for 2013
b. The tablet sales are seasonal, with the following quarterly indexes:
What is the quarterly sales projection for 2013
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Q 7Q 7
A manufacturer of computer workstations gathered average monthly sales figures from its 56 branch offices and dealerships across the country and estimated the following demand for its product:
Q = +15,000 - 2.80 P + 150 A + 0.3 P pc + 0.35 P m + 0.2 P c
(5,234) (1.29) (175) (0.12) (0.17) (0.13)
R 2 = 0.68 SEE = 786 F = 21.25
The variables and their assumed values are
Q = Quantity
P = Price of basic model = 7,000
A = Advertising expenditures (in thousands) = 52
P pc = Average price of a personal computer = 4,000
P m = Average price of a minicomputer = 15,000
P c = Average price of a leading competitor's workstation = 8,000
a. Compute the elasticities for each variable. On this basis, discuss the relative impact that each variable has on the demand. What implications do these results have for the firm's marketing and pricing policies
b. Conduct a t -test for the statistical significance of each variable. In each case, state whether a one-tail or two-tail test is required. What difference, if any, does it make to use a one-tail versus a two-tail test on the results Discuss the results of the t -tests in light of the policy implications mentioned.
c. Suppose a manager evaluating these results suggests that interest rates and the performance of the computer (typically measured in millions of instructions per second, or MIPS) are important determinants of the demand for workstations and must therefore be included in the study. How would you respond to this suggestion Elaborate.
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Q 8Q 8
The sales data over the last 10 years for the Acme Hardware Store are as follows:
a. Calculate the compound growth rate for the period of 2003 to 2012.
b. Based on your answer to part a, forecast sales for both 2013 and 2014.
c. Now calculate the compound growth rate for the period of 2007 to 2012.
d. Based on your answer to part c, forecast sales for both 2013 and 2014.
e. What is the major reason for the differences in your answers to parts b and d If you were to make your own projections, what would you forecast (Drawing a graph is very helpful.)
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Q 9Q 9
You are given the following demand for European luxury automobiles:
Q = 1,000 P -0.93 P A 0.75 P J 1.2 I 1.6
where P = Price of European luxury cars
P A = Price of American luxury cars
P J = Price of Japanese luxury cars
I = Annual income of car buyers
Assume that each of the coefficients is statistically significant (i.e., that they passed the t -test). On the basis of the information given, answer the following questions:
a. Comment on the degree of substitutability between European and American luxury cars and between European and Japanese luxury cars. Explain some possible reasons for the results in the equation.
b. Comment on the coefficient for the income variable. Is this result what you would expect Explain.
c. Comment on the coefficient of the European car price variable. Is that what you would expect Explain.
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Q 10Q 10
The Miracle Corporation had the following sales during the past 10 years (in thousands of dollars):
a. Calculate a trend line, and forecast sales for 2013. How confident are you of this forecast
b. Use exponential smoothing with a smoothing factor w = 0.7. What is your 2013 forecast How confident are you of this forecast
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Q 11Q 11
You have the following data for the last 12 months' sales for the PRQ Corporation (in thousands of dollars):
a. Calculate a 3-month centered moving average.
b. Use this moving average to forecast sales for January of next year.
c. If you were asked to forecast January and February sales for next year, would you be confident of your forecast using the preceding moving averages Why or why not
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Q 12Q 12
Office Enterprises (OE) produces a line of metal office file cabinets. The company's economist, having investigated a large number of past data, has established the following equation of demand for these cabinets:
Q = 10,000 + 60 B - 100 P + 50 C
where Q = Annual number of cabinets sold
B = Index of nonresidential construction
P = Average price per cabinet charged by OE
C = Average price per cabinet charged by OE's closest competitor
It is expected that next year's nonresidential construction index will stand at 160, OE's average price will be $40, and the competitor's average price will be $35.
a. Forecast next year's sales.
b. What will be the effect if the competitor lowers its price to $32 If it raises its price to $36
c. What will happen if OE reacts to the decrease mentioned in part b by lowering its price to $37
d. If the index forecast was wrong, and it turns out to be only 140 next year, what will be the effect on OE's sales
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Q 13Q 13
An economist has estimated the sales trend line for the Sun Belt Toy Company as follows:
S t = 43.6 + 0.8 t
S t represents Sun Belt's monthly sales (in millions of dollars), and t = 1 in January 2008. The monthly seasonal indexes are as follows:
Forecast monthly sales for the year 2013.
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Q 14Q 14
The MNO Corporation is preparing for its stockholder meeting on May 15, 2013. It sent out proxies to its stockholders on March 15 and asked stockholders who plan to attend the meeting to respond. To plan for a sufficient number of information packages to be distributed at the meeting, as well as for refreshments to be served, the company has asked you to forecast the number of attending stockholders. By April 15, 378 stockholders have expressed their intention to attend. You have available the following data for the last 6 years for total attendance at the stockholder meeting and the number of positive responses as of April 15:
a. What is your attendance forecast for the 2013 stockholder meeting
b. Are there any other factors that could affect attendance, and thus make your forecast inaccurate
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Q 15Q 15
In the Columbia Gas of Ohio study that forecasted the demand for gas (see p. 155), the company developed the following coefficients for their equation:
Forecast the demand for gas for a day, when the expected average temperature will be 40 degrees, the prior day's average temperature was 37, and the average wind speed is predicted to be 8 miles per hour.
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Q 16Q 16
Explain the difference between time series data and cross-sectional data. Provide examples of each type of data.
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Q 17Q 17
"The best forecasting method is the one that gives the highest proportion of correct predictions." Comment.
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Q 18Q 18
Would there be any differences in the set of variables used in a regression model of the demand for consumer durable goods (e.g., automobiles, appliances, furniture) and a regression model of the demand for "fast-moving consumer goods" (e.g., food, beverages, personal care products) Explain.
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Q 19Q 19
Enumerate methods of qualitative and quantitative forecasting. What are the major differences between the two
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Q 20Q 20
Briefly explain the meaning of R 2. A time series analysis of demand tends to result in a higher R 2 than one using cross-sectional data. Why do you think this is the case
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Q 21Q 21
Discuss the benefits and drawbacks of the following methods of forecasting:
a. Jury of executive opinion
b. The Delphi method
c. Opinion polls
Each method has its uses. What are they
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Q 22Q 22
Summarize the steps involved in conducting the t -test. What is the basis for using the "rule of 2" as a convenient method of evaluating t -ratios
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Q 23Q 23
Why are manufacturers' new orders, nondefense capital goods, an appropriate leading indicator
b. Why is the index of industrial production an appropriate coincident indicator
c. Why is the average prime rate charged by banks an appropriate lagging indicator
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Q 24Q 24
Briefly explain the meaning of the F -test. Why do you think this test is considered to be more important in multiple regression analysis than it is in simple regression analysis
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Q 25Q 25
Discuss some of the important criticisms of the forecasting ability of the leading economic indicators.
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Q 26Q 26
What is multicollinearity How can researchers detect this problem What is the impact of this problem on the regression estimates What steps can be taken to deal with this problem
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Q 27Q 27
Manhattan was allegedly purchased from Native Americans in 1626 for $24. If the sellers had invested this sum at a 6 percent interest rate compounded semiannually, how much would it amount to today
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Q 28Q 28
What is the identification problem What effect will this problem have on the regression estimates of a demand function Explain
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Q 29Q 29
The compound growth rate is frequently used to forecast various quantities (sales, profits, and so on). Do you believe this is a good method Should any cautions be exercised in making such projections
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Q 30Q 30
Describe projections that use either moving averages or exponential smoothing. Under what conditions can these techniques be used Which of the two appears to be the more useful
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Q 31Q 31
How do econometric models differ from "naive" projection methods Is it always advisable to use the former in forecasting
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Q 32Q 32
You have been asked to produce a forecast for your company's product, bottled water. Discuss the kind of information you would look for in order to make this forecast.
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Q 33Q 33
The following are the monthly changes in the index of leading economic indicators during 2001 and January 2002:
January +.1 August 0
February +.1 September .6
March .3 October +.1
April .1 November +.8
May +.6 December +1.3
June +.2 January 2002 +.6
July +.3
What would be your prediction for the U.S. economy in 2002
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