Statistics HW
nataliejag
lesson_8-_hw_part_2.docxInstructions:
Download and read the Regression Experiment and answer the questions in part C of the document titled Analysis and Interpretation.
After working through the problems, go to Lesson 8: Individual Exercises 8 and answer the associated multiple choice questions.
Regression Experiment: An Overview of Model Development and Interpretation
THE DEMAND FOR ROSES
A. The Market for Roses
Roses have an almost universal identification with the act of sending flowers, and consequently, they are one of the major products that the retail florist sells either alone or as part of floral arrangements. The wholesale cut flower supplier must therefore be able to supply roses to retail florists. However, a number of factors have recently affected the growth in demand for roses. First, there has been a general breakdown of "old country social customs" such as the tradition of always sending flowers to funerals. Second, there has been a growth in demand for competing products, such as carnations and wild flowers, which live longer than roses. Likewise, there has been increased use by retailers of other flowers that are larger and require smaller quantities per arrangement. Also, in this context, there has been accelerated growth in the demand for green plants. Green plant sales only accounted for 22 percent of the total sales for the floral industry in 1975, but had jumped to 42 percent by 1984, and are predicted to rise above 50 percent in the 1990s. Third, the costs of growing roses have been increasing significantly.
B. Developing a Demand Function (Model) for Roses
Matthew’s and Sons is wholesale supplier of rose to retail florists in the Detroit metropolitan area. This firm is concerned with developing a model that will aid in forecasting rose sales (Qt) and developing appropriate strategies for the firm's operations. Data on Matthew’s rose sales over the past sixteen quarters was available from their monthly sales summaries. See Table 1 for data on variables that Matthew and Sons thought would be key to their demand analysis.
Price data for roses and carnations was available form Matthew and Sons' billing records; unemployment data for the Detroit area was available in the Michigan Manpower Review; information on births, deaths, and marriages ("flower events") was obtained from the Michigan Department of Health; average family income is available from the U.S. Department of Labor.
C. Analysis and Interpretation
1. Your task is to use the data in Table 1 to develop a demand model for Matthew and Sons' sales of roses. It would be a great learning experience to try and do this on your own first, then use my suggestions below to compare your analysis to mine. Note: you should begin by including the price of roses (RosePr), the price of carnations (CarnatPr) and the trend variable (time) as well as a constant (i.e. an intercept). Then explain the expected sign (+, -, or ?) for each of those variables as well as any other variables you deem appropriate to include in your model. Finally, use multiple regression to estimate the coefficients for your model.
2. To what extent was multicollinearity a problem in choosing an appropriate model to estimate? Use theory and computer output to support your answer.
3. Run a regression using the following variables: price of roses (Rosepr), the price of carnations (CarnatPr), the trend variable (time), Births, Deaths, Wedding, Unemp, Income as well as a constant. Describe each variable coefficient as insignificant, significant at .10, significant at .05 or significant at .01 and whether you used a one- or two-tail test and why. What is the advantage of using Births, Deaths and Wedding instead of just Events? Would it be wise to include Events and also Births, Deaths and Wedding?
4. Interpret precisely the parameter (coefficient) associated with the price of roses.
5. Calculate and interpret the price elasticity for roses. Using elasticity formula from iMBA 501: Ep=%change in dozen / %change in rosepr = Δdozen/ ΔQrosepr x mean rosepr/mean dozen = price coefficient x mean rosepr/mean dozen.
6. What level of substitutability exists between roses and carnations? Provide support for your answer.
7 What is the R2 of your model? Interpret its magnitude.
8. Is the apparent explanatory power of the model as indicated by the value of R2 statistically significant? Do the appropriate F-test to confirm or refute.
9. Interpret the coefficient on the trend variable. Why may such a result have occurred?
10. Suppose the florists believe that first-quarter sales are greater than sales in any other quarter. Create and define a variable(s) that will allow you to test this hypothesis. Re-estimate the equation with your new variable. Are the florists correct about first-quarter sales?
11. What are some of the shortcomings of this model? What variable(s) may have been omitted from this model?
Table 1
Demand for Roses Data
You can copy this data and paste directly in Excel.
Births, Deaths, and Weddings are flower events. Events = Births + Deaths + Weddings.
CarnatPr = the price of a dozen carnations.
RosePr = the price of a dozen roses.
Dozen = the number of roses sold (in dozens).
Time = trend variable.
Unemp = unemployment rate.
Income = Average family income ($100 units)
Questions:
Run a regression using the following variables: price of roses (Rosepr), the price of carnations (CarnatPr), the trend variable (time), Births, Deaths, Wedding, Unemp, Income as well as a constant. Answer questions 1-10 based on this model.
1.
Which of the following is true of the expected coefficients in the model?
A) Births, deaths, wedding, price of carnations, and income are expected to be positive and the price of roses and unemployment are expected to be negative.
B) Births, deaths, wedding, and income are expected to be positive and the price of roses, price of carnations, and unemployment are expected to be negative.
C) Price of carnations and income are expected to be positive and births, deaths, wedding, the price of roses and unemployment are expected to be negative.
D) none of the above
2.
The price elasticity for roses is approximately
A) -10.9
B) -3.7
C) -1.9
D) none of the above
3.
The cross price elasticity for roses and carnations is approximately
A) 2.0
B) 3.2
C) 4.5
D) none of the above
4.
The coefficient associated with the price of roses can be interpreted as follows: For every $1 increase in the price of a dozen roses, there are 2526.23 dozen less sold holding all other variables constant.
A) True
B) False
5.
The estimated coefficient for wedding is found to be approximately
A) 0.47 and is insignificant.
B) 0.12 and is significant at the .01 level.
C) -0.29 and is insignificant.
D) none of the above.
6.
The estimated coefficient for Deaths is found to be insignificant and therefore should be dropped from the regression model.
A) True
B) False
7.
Which of the following pairs of variables exhibits the highest degree of multicollinearity?
A) wedding and events
B) births and events
C) income and unemployment
D) none of the above.
8.
Which of the following statements best represents the interpretation of the R2 for this model?
A) The variables included in the model explain 91.9% of the variation in the number of dozens of roses sold.
B) The variables included in the model explain 97.9% of the variation in the number of dozens of roses sold.
C) The variables included in the model explain 95.5% of the variation in the number of dozens of roses sold.
D) none of the above
9.
Which of the following statements best represents the interpretation of the explanatory power of the R2 for this model?
A) The F-critical is greater than the F-statistic so we can reject the null hypothesis of no explanatory power for the model.
B) The F-critical is less than the F-statistic so we cannot reject the null hypothesis of no explanatory power for the model.
C) The F-critical is greater than the F-statistic so we cannot reject the null hypothesis of no explanatory power for the model.
D) none of the above
10.
According to the coefficient associated with the trend variable, the number of dozens of roses sold was decreasing at a rate of 472.67% per quarter more than could be explained by changes in the other variables.
A) True
B) False
Suppose the florists believe that first-quarter sales are greater than sales in any other quarter. Create and define a variable(s) that will allow you to test this hypothesis. Re-estimate the equation with your new variable and answer question 11.
11.
The florists are correct about the first-quarter sales being greater than sales in any other quarter.
A) True
B) False
12.
A potential shortcoming of this model could be
A) the high degree of substitutability between the price of roses and the price of carnations
B) multicollinearity between sales of roses and the price of carnations
C) an omitted variable such as green plant price
D) none of the above
