Making an algebraic equation from statistical results - FreeEconHelp.com, Learning Economics... Solved!

## 9/27/11

This post will go over the transformation process of statistical results, and show how to derive an algebraic function from your results table.

You have just been hired by Gameday Sportswear, a large producer of college football apparel. Your boss has given you the regression below, and wants you to answer the following questions.
Estimated Demand Function
Dependent Variable is QJ

 Variable Coefficient T-Stat Constant (C) 105.05 1.874 Real price of college football jerseys (PF) -1.8 -3.961 Real price of NFL jerseys (PNFL) -1.1 -3.214 Real Advertising Expenditure (A) 2.6 4.025 Income (Inc) 1.9 3.848 R^2 0.655

Estimated Supply Function
Dependent Variable is QJ

 Variable Coefficient T-Stat Constant (C) 30.1 0.943 Real price of college football jerseys (PF) 4.6 3.438 Real price of materials (PM) -8.3 -3.268 Real labor wage (PL) -4.6 -4.914 Technology Index (T) 12.5 2.199 R^2 0.741
Description of Variables
Variable Definition Average
C Constant
QJ Quantity of football jerseys produced and sold (1,000 units)
PF Real price of college football jerseys
PNFL Real price of NFL jerseys \$40
PM Real Price of materials \$4
PL Real Labor Wage \$16
A Real Advertising Expenditure (\$1,000s) \$90
Inc Real Income (\$1,000s) \$34
T Tech. Index 18

1. What is the estimated demand function equation for Gameday football jerseys?
The estimated demand function will take the general regression format of Y = B1X1 + B2X2 + B3X3 etc.

So in this particular case it will look like:

QJ = B1C + B2 PF + B3 PNFL + B4 A + B5 Inc

The B’s represent the coefficients associated with each independent variable, and they are estimated to show how a change in that particular variable will affect our dependent variable QJ.

2. What is the estimated supply function equation for Gameday football jerseys?

The supply function written in algebraic form will look like:

QJ = B1C + B2 PF + B3 PM + B4 PL + B5 T

Keep in mind that we are doing things backwards in this particular problem.  Normally you make the algebraic function first (what independent variables that you think will impact your dependent variable) and then you run your regression analysis to find values for your coefficients and their associated T-stats.