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 |
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.
