QUESTION ONE (30 MARKS)

1. The following data shows observations on recent home sales in Nakuru town. The variables listed are selling price (in shillings), size of house (in square feet) and annual property taxes (in shillings).

Selling Price	Size	Taxes
27,990,000	2048	310,400
14,650,000	912	117,300
23,770,000	1654	307,600
20,000,000	2068	160,800
159,90000	1477	145,400
49,990,000	3153	299,700
26,550,000	1355	405,400

Required:

i.) Fit a regression model to estimate the selling price using house size and annual property taxes. [4 Marks]

ii.) Are the signs of the slope coefficients of the independent variables as one would expect? Explain briefly. Also interpret the estimated slope coefficients. [3 Marks]

iii.) Use p-values test if the estimated slope coefficients are significantly different from zero at the 1% level of significance. [3 Marks]

iv.) Test the null hypothesis that the two independent variables taken together, do not linearly affect the selling price of a house. [3 Marks]