Data on the quantity demanded of a commodity (in kg), the price of that commodity (in USD) and the level of income (in USD) are given below:

Let the demand function be given by, ????1 ????2 ????i i i i q = Ap in e , where q = per capita consumption of a commodity, p = price per unit of the commodity, in = per capita disposable income.
Requirements:
(i) Show that ????1 is the elasticity of demand with respect to price and ????2 is the elasticity of demand with respect to income.
(ii) Discuss the method to estimate the parameters.
(iii) Estimate the non-linear equation ????1 ????2 ????i i i i q = Ap in e and comment on your obtained results.
(iv) Test the null hypothesis 0 j H : ???? ???? 0, ( j =1, 2) against a suitable alternative hypothesis.
(v) Find, the 95% confidence interval for parameters.
(vi) Calculate TSS, RSS and ESS.
(vii) Calculate the value of the coefficient of determination and comment on your obtained results.
(viii) Find, Adjusted(R2 ) and compare with R2 .

Quantity Demanded (g) Price (p) Income (in) 100 5 1000 75 7 600 80 6 1200 70 6 500 50 8 300 65 90 100 110 60 75 65 7543967 400 1300 1100 1300 300 450 350