Capps AGEC 317 Fall 2013

Problem Set 4

Consider units sold and personal selling expenditures for the firm Electronic Data Processing, Inc. (EDP) for calendar year 2010.

Month / Units Sold / Personal Selling Expenditures ($)
January / 2,500 / 43,000
February / 2,250 / 39,000
March / 1,750 / 35,000
April / 1,500 / 34,000
May / 1,000 / 26,000
June / 2,500 / 41,000
July / 2,750 / 40,000
August / 1,750 / 33,000
September / 1,250 / 26,000
October / 3,000 / 45,000
November / 2,000 / 32,000
December / 2,000 / 34,000

(a)Describe this type of data set.

(b) Consider the demand relation between units sold and personal selling expenditures. Let U = units sold and PSE = personal selling expenditures.

(i)Plot actual EDP unit sales over calendar year 2010. Describe the plot of these data.

(ii)Plot actual EDP unit sales on the y-axis and personal selling expenditures on the x-axis. What is the technical name of this plot?

(c)Retrieve descriptive statistics using SAS. Specifically obtain the mean, median, variance, standard deviation, minimum, maximum, coefficient of variation, skewness, and kurtosis values for U and PSE.

(d) What is the degree of correlation between U and PSE?

(e)Square the correlation between U and PSE.

(f)Using Ordinary Least Squares procedures, estimate the following regression model:

Ut = b0 + b1PSEt + et

Verify that b0 = -1292.3 and that b1 = 0.09289. Interpret this estimate of b1.

Also, verify that R2 = 0.878 and that = 0.865.

(g)Compare the R2 value obtained in (f) with the square of the correlation coefficient between U and PSE obtained in (e).

(h)Obtain the predicted values and residuals from this regression.

(i)Now, using Ordinary Least Squares procedures, estimate the following regression model:

lnUt = c0 + c1lnPSEt + vt

Obtain estimates of c0 and c1. Interpret the estimate of c1.

Problem ST5.2 on p.188 of Hirschey.

Problem 5.7 on pp.192-193 of Hirschey.

Problem 5.9 on p.194 of Hirschey.

Do the case study problem (Mrs. Smyth’s pies) on pp.195-197 of Hirschey.

6. Given the information in the following table,

Year / Quantity Sold / Price / Advertising Expenditures / Disposable Income
1995 / 42,100 / 11.77 / 46,100 / 38,000
1996 / 55,500 / 9.96 / 47,200 / 39,100
1997 / 71,100 / 12.36 / 60,900 / 40,100
1998 / 63,200 / 12.49 / 55,600 / 44,200
1999 / 77,200 / 10.68 / 64,400 / 41,800
2000 / 70,900 / 12.07 / 60,700 / 44,800
2001 / 55,600 / 11.97 / 52,100 / 39,900
2002 / 70,700 / 11.23 / 57,900 / 41,700
2003 / 71,400 / 11.26 / 55,600 / 41,200
2004 / 79,400 / 9.79 / 60,100 / 41,200
2005 / 60,600 / 12.29 / 50,700 / 44,000
2006 / 50,800 / 12.7 / 46,500 / 43,300
2007 / 61,800 / 12.33 / 58,600 / 41,000
2008 / 40,500 / 10.88 / 42,800 / 38,300
2009 / 85,300 / 10.14 / 64,800 / 42,100

(a)Estimate a linear in logs demand function. That is,

(b)Is the demand for this product elastic, inelastic, or unitary elastic? Is the product inferior, a necessity, or a luxury? If advertising expenditures increase by 10 percent, all other factors held constant, what happens to the quantity sold of the good in question?

(c)What proportion of variation in quantity sold is accounted for by the model adjusted for degrees of freedom?

(d)If for year 2010, P = $10, ADVEXP = 50,000, and DISPINC = 42,000, predict the quantity sold for 2010.

7. Use the data set concerning production of output from labor and capital.

Formulate the following model specification

log_outputi = a0 + a1log_labori + a2log_capitali + vi

The subscript i denotes the firm number i = 1, 2, …, 25.

Using SAS,

(a)Obtain the descriptive statistics of output, labor, and capital, specifically means, medians, standard deviations, minima, maxima, and coefficient of variations.

(b)Estimate the model specification using OLS.

(c)Interpret the estimated coefficients.

(d)Obtain the 90% confidence limits associated with the estimated parameters of labor and capital.

(e)Test H0: a1 = a2. To what does this hypothesis relate? Also test H0: a1+ a2 =1. To what does this hypothesis relate?

(f)Determine if the residuals follow a normal distribution. Why is this test of hypothesis important? What is the technical name of this test statistic?

8. Using the Construction data, set up the SAS program to estimate the model specification given as CONTRCTSt = a0 + a1INTRATEt +a2HSTARTSt +u, where

CONTRCTS / is total U.S. construction contracts in millions of dollars.
INTRATE / is the average new home mortgage rate (%).
HSTARTS / is the number of private housing starts in thousands of units.

(a)Plot each of the variables over time (January 1983 to October 1989).

(b)Provide scatter plots of CONTRCTSt vs INTRATEt and HSTARTSt and INTRATEt.

(c)Obtain the pair wise correlations of CONTRCTSt, INTRATEt, and HSTARTSt.

(d)Evaluate the model in terms of goodness-of-fit. Find the within-sample root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE).

(e)Re-estimate the model, holding out the last 12 observations.

(f)Evaluate the forecasting ability of the model based on the last 12 observations in terms of root mean squared error (RMSE), mean absolute error (MAE), and mean absolute percent error (MAPE).

(g)Estimate the original model but now also accounting for seasonality. Test whether or not seasonality affects CONTRCTS.

9. Revisit Problem 1 but include price and advertising expenditures into the regression model. The extended data set is on the AGEC 317 website. Estimate the regression model:

Ut = a0 + a1PRICEt +a2ADEXPt + a3PSEt + et

Also estimate lnUt = f0 + f1lnPRICEt+f2lnADEXPt + f3lnPSEt + vt.

Compare and contrast the results.