Given the following data, find the Demand equation where P is the y variable, and Q is the x variable [P = f(Q)].
Q |
P |
180 |
475 |
590 |
400 |
430 |
450 |
250 |
550 |
275 |
575 |
720 |
375 |
660 |
375 |
490 |
450 |
700 |
400 |
210 |
500 |
Regression Summary Output is as follows.
SUMMARY OUTPUT | ||||
Regression Statistics | ||||
Multiple R | 0.8657 | |||
R Square | 0.7495 | |||
Adjusted R Square | 0.7182 | |||
Standard Error | 37.4321 | |||
Observations | 10 | |||
ANOVA | ||||
df | SS | MS | F | |
Regression | 1 | 33540.69576 | 33540.7 | 23.93775 |
Residual | 8 | 11209.30424 | 1401.163 | |
Total | 9 | 44750 | ||
Coefficients | Standard Error | t Stat | P-value | |
Intercept | 585.0911 | 29.1051 | 20.1027 | 0.0000 |
Q | -0.2888 | 0.0590 | -4.8926 | 0.0012 |
Therefore:
(1) Demand equation: P = 585.0911 - 0.2888 x Q
(2) Total revenue (TR) = P x Q = 585.0911Q - 0.2888 x Q2
(3) Marginal revenue = dTR/dQ = 585.0911 - 0.5776 x Q
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