Question

the table below shows the price quantity of demanded of packaged of pure water in nigeria. price in # = 0.5, 0.6, 0.7, 0.8, 0.8, 0.9. Quantity Demand = 160, 140, 120, 110, 90, 80. Let Xi represent the price change per unit and Yi represent the quantity demand at that price. The demand function may be postulated as; Yi =a+bXi + ei . FIND THE OLS ESTIMATE OF THE DEMAND FUNCTION AND var(a), var(b) and their respective standard error , Compute the value of the coefficient of determination (r^2) and f-statistic of the model

Answer 1

	X (price change per Unit) xi	Quantity Demand yi	xi^2	yi^2	xi*yi
	0.5	160	0.25	25600	80
	0.6	140	0.36	19600	84
	0.7	120	0.49	14400	84
	0.8	110	0.64	12100	88
	0.8	90	0.64	8100	72
	0.9	80	0.81	6400	72
Sum	4.3	700	3.19	86200	480
Average	0.72	116.67

S_xx = 0.108

S_yy = 4533.33

S_xy = -21.67

Regression equation Yi =a+bXi + ei

b = S_xy / S_xx = -200.0

a = = 116.0 - 0.72* (-200) = 260

Equation will be Yi =260 - 200Xi + ei

	Coefficients	Standard Error	t Stat	P-value
Intercept	260	15.66476	16.59777	7.72E-05
X (price change per Unit)	-200	21.48345	-9.30949	0.000741

ANOVA
	df	SS	MS	F	Significance F
Regression	1	4333.333	4333.333	86.66667	0.000741
Residual	4	200	50
Total	5	4533.333

R-square = = 0.959

Model explains 95.9 % variability between the data.