Question

Estimate the demand curve using regression analysis. Write down the equational form. Interpret the coefficients, statistical significance and R2. What are the limitations of your specification (omitted variables, correlation vs. causality)?

Quantity	Price
84	59
80	65
85	54
83	61
81	64
84	58
87	48
78	68
82	63
76	70
79	65
75	80

Answer 1

The regression output from Excel is given below:

The equation of demand curve is:

Quantity = 108.57 - 0.44*Price

Interpretation:

Intercept - When Price = 0, Qunatity = 108.57 units.

Slope - When price increases by 1 unit, the quantity demanded decreases by 0.44 units.

R² = 0.9161 i.e. 91.61% of the variation in the dependent variable Quantitiy is explained by the independent variable Price.

Statistical Significance:

When p-value is less than 0.05, the variable is significant at 5% level of significance.

Intercept: p-value = 1.74E-12 ~ 0.00 < 0.05, the intercept is significant.

Slope: p-value = 1.06E-06 ~ 0.00 < 0.05, the slope coefficient is significant.

Limitations of the specification:

According to economic theory, demand depends on variables other than price only. Demand depends on factors like price of substitutes/complements, income, tastes and preferences. Thus, the model lacks important variables on which demand depends, thus there are omitted variables in the model.