Economics Math: Correlations / Linear & Multiple Regression

Correlations/Linear & Multiple Regression
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A golf club manufacturer is trying to determine how the price of a set of clubs affects the demand for clubs. The file P10_50.xlsx contains the price of a set of clubs and the monthly sales. Assume the only factor influencing monthly sales is price. Fit the following three curves to these data: linear (Y = a + bX), exponential (Y = abX), and multiplicative (Y = aXb). Which equation fits the data best?Interpret your best-fitting equation.
Assume the only factor influencing monthly sales is price. Fit the following three curves to these data: linear (Y = a + bX), exponential (Y = abX), and multiplicative (Y = aXb). Which equation fits the data best? 470.
Linear (Y = a + bX)
Regression line equation: y=50579.32-70.79x
Where Y is demand and x is price
When price is $ 470 the sales is 50579.32-70.79x=17,308
SUMMARY OUTPUT











Regression Statistics





Multiple R

0.948677





R Square

0.899989





Adjusted R Square

0.887488





Standard Error

3251.334





Observations

10











ANOVA






 

df

SS

MS

F

Significance F

Regression

1

7.61E+08

7.61E+08

71.99113

2.85239E-05

Residual

8

84569378

10571172



Total

9

8.46E+08

 

 

 







 

Coefficients

Standard Error

t Stat

P-value

 

Intercept

50579.32

3612.023

14.00304

6.56E-07


X Variable 1

-70.7935

8.343613

-8.48476

2.85E-05

 

Exponential (Y = abX)
To get the equation We take the natural logarithms of the Y values ro give the model
Ln(Y)= 11.51-0.00399X
Y=e--0.004X+11.51
Then y= 99717.85* 0.99602x
A= 99717.85
B= 0.996
When price is $ 470 the sales is 99717.85* (0.99602^470) = 15,302
SUMMARY OUTPUT











Regression Statistics





Multiple R

0.9995076





R Square

0.999015443





Adjusted R Square

0.998892373





Standard Error

0.017248693





Observations

10






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