Transcript The K-Variable Model Hamburger chain

The K-Variable Model
Hamburger chain
What’s the effect of prices and
advertising on revenues?
Data: 52 weeks
TR = Weekly revenue (in $1000)
P = Price (in $)
A = Advertising ( in $1000)
Econometria. Walter Sosa Escudero
Dependent Variable: TR
Method: Least Squares
Date: 03/24/00 Time: 18:53
Sample: 1 52
Included observations: 52
Variable
C
P
A
Coefficient
Std. Error
t-Statistic
Prob.
104.7855
-6.641930
2.984299
6.482719
3.191193
0.166936
16.16382
-2.081331
17.87689
0.0000
0.0427
0.0000
R-squared
Adjusted R-squared
0.867085
0.861660
Mean dependent var
S.D. dependent var
120.3231
16.31873
S.E. of regression
Sum squared resid
6.069611
1805.168
Akaike info criterion
Schwarz criterion
6.500427
6.612999
Log likelihood
Durbin-Watson stat
-166.0111
2.040793
F-statistic
Prob(F-statistic)
159.8280
0.000000
Econometria. Walter Sosa Escudero
Dependent Variable: TR
Method: Least Squares
Date: 03/24/00 Time: 18:53
Sample: 1 52
Included observations: 52
Variable
C
P
A
Coefficient
Std. Error
t-Statistic
Prob.
104.7855
-6.641930
2.984299
6.482719
3.191193
0.166936
16.16382
-2.081331
17.87689
0.0000
0.0427
0.0000
R-squared
Adjusted R-squared
0.867085
0.861660
Mean dependent var
S.D. dependent var
120.3231
16.31873
S.E. of regression
Sum squared resid
6.069611
1805.168
Akaike info criterion
Schwarz criterion
6.500427
6.612999
Log likelihood
Durbin-Watson stat
-166.0111
2.040793
F-statistic
Prob(F-statistic)
159.8280
0.000000
An increase in price of $1 will lead to a fall in weekly revenue
of $6,642. Or, a reduction in price of $1 will lead to an increase
in revenue of $6,642.
An increase in advertising expenditure of $1,000 will lead to
an increase in total revenue of $2,984. 3.
Adverstising seems to be statistically significant to explain
revenues. Is price really significant?
Econometria. Walter Sosa Escudero
• The estimated intercept implies that if both price and advertising
expenditure were zero the total revenue earned would be
$104,790. This is obviously not correct. In this model, as in many
others, the intercept is included in the model for mathematical
completeness and to improve the model’s predictive ability.
• Remark: A word of caution is in order about interpreting regression
results. The negative sign attached to price implies that reducing
the price will increase total revenue. If taken literally, why should
we not keep reducing the price to zero? This makes the following
important point: estimated regression models describe the
relationship between the economic variables for values similar to
those found in the sample data. Extrapolating the results to
extreme values is generally not a good idea. In general, predicting
the value of the dependent variable for values of the explanatory
variables far from the sample values invites disaster.
• R2 : 86.7% of the variation in total revenue is explained by the
variation in price and by the variation in the level of advertising
expenditure.
Econometria. Walter Sosa Escudero
Econometria. Walter Sosa Escudero
Econometria. Walter Sosa Escudero