BA 2004 Managerial Economics
Demand Theory and Estimation
Electronix Inc. Case
Using SPSS, MS Excel or other statistical software package, run the given data
and answer the following in MS Word.
Assume that Electronix, Inc., a small startup company that distributes a particular
business machine, has the following monthly data on unit sales (Q), price (P),
advertising expenditures (AD), and personal selling expenditures (PSE) over the
past year.
If a linear relation between unit sales, price, advertising, and personal selling
expenditures is hypothesized, the regression equation takes the following form:
Sales y t =b o+ b P Pt + b AD AD t + b PSE PSE t +u t
where y is the number of units sold, P is the average price per month, AD is
advertising expenditures, PSE is personal selling expenditures, and u is a
random disturbance term – all measured on a monthly basis over the past year.
A. Present the computer results of regression.
B. Estimate the regression equation of y on the explanatory variables.
C. Check for consistency in the relationship between quantity demand and the
three explanatory variables as postulated in demand theory by indicating the
change in the quantity demanded of the commodity for each unit change in
the explanatory variables.
D. Find and interpret the adjusted and the unadjusted coefficient of
determination.
E. Test at the 5% level for the overall statistical significance of the regression.
Interpret the result.
F. Test at the 5% level for the statistical significance of the slope parameters.
Interpret the result.
G. Specify the final demand model.
H. Estimate the confidence intervals for y if P = $2,500, AD = $30,000 and PSE =
$50,000.
Interpret your forecast. (Tip: SEE provides a helpful means for estimating
confidence intervals)
Show all results in two decimal places.
Advertising
Personal Selling
Month Units Sales Price ($) Expenditures
Expenditures ($)
($)
January 2,500 3,800 26,800 43,000
February 2,250 3,700 23,500 39,000
March 1,750 3,600 17,400 35,000
April 1,500 3,500 15,300 34,000
May 1,000 3,200 10,400 26,000
June 2,500 3,200 18,400 41,000
July 2,750 3,200 28,200 40,000
August 1,750 3,000 17,400 33,000
September 1,250 2,900 12,300 26,000
October 3,000 2,700 29,800 45,000
November 2,000 2,700 20,300 32,000
December 2,000 2,600 19,800 34,000
The Summary Outputs for Regression Analysis derived by using MS Excel are
presented in the image above.
Regression Equation:
Y = -117.513 – 0.296 X1 + 0.036 X2 + 0.066 X3
Y = Unit Sales
X1= Price
X2= Advertising Expenditures
X3=Personal Selling Expenditures
The coefficient of determination in this case is 0.969720166, which means that
the X Variables account for 96.97 percent of the variation in the Y Variable.
Because there are multiple X Variables, the Adjusted R Squared is the most
precise percentage that can explain the variation in the Y Variable (Unit Sales).
As a result, the Price, Advertising Expenditures, and Personal Selling
Expenditures account for 95.84 percent of the variation in Unit Sales.
Prob > F = 2.04356E-06 or 0.00000204356; which is < 0.05
We Reject H0 or Reject the Null Hypothesis if we assess the overall statistical
level of significance of regression at 5%. As a result, the x (Unit Sales) and y
variables have a significant relationship (Price, Advertising Expenditures,
Personal Selling Expenditures).
There is a significant relationship between Unit Sales and Price because the P-
value of Price (0.019647168) is less than the (0.05).
There is no significant relationship between Unit Sales and Advertising
Expenditures because the P-value of Advertising Expenditures (0.32666239) is
greater than the (0.05).
There is a significant relationship between Unit Sales and Personal Spending
Expenditures since the P-value of Personal Spending Expenditures
(0.001740562) is less than the (0.05).
As a result, Price and Personal Spending Expenditures can predict the Unit
Sales for business machines of the Electronix Inc. over the past year. Meanwhile,
Advertising Expenditures cannot predict the Unit Sales.
If X1 = 2500; X2 = 30000; X3 = 50000
Y = -117.513 – 0.296 X1 + 0.036 X2 + 0.066 X3
Y = -117.513 – 0.296 (2500) + 0.036 (30000) + 0.066 (50000)
Y = -117.513 – 740 + 1080 + 3300
Y = 3,522.49
Therefore, the predicted Unit Sales is $3,522.49 if the Price is $2,500, AD is
$30,000, and PSE is $50,000.
