Question

The commercial division of a real estate firm conducted a study to determine the extent of the relationship between annual gross rents ($1000s) and the selling price ($1000s) for apartment buildings. Data were collected on several properties sold. The data is...

	df	SS	MS	F	Significance F
Regression	1	41976.4
Residual	7
Total	8	52373.2
	Coefficients	Standard Error	t Stat	P-value
Intercept	19	3.2213	6.21
Annual Gross Income	7.75	1.457806668	5.31620562

(a) How many apartments are there?
(b) Write the estimated regression equation
(c) Use the t-test to determine whether the selling price is related to annual gross rents. Use a=0.05
(d) Use the f-test to determine whether the selling price is related to annual gross rents. Use a=0.05
(e) Predict the selling price of an apartment building with gross annual rents of $52500

Answer 1

a)

here as degree of freedom of residual n-2=7

hence number of apartments =n+2=7+2=9

b)

frm above estimated regression equation: Yhat =19+7.75*x

where Yhat is estimated selling price corresponding to x , annual gross income.

c)null hypothesis:Ho: =0

alternate hypothesis :Ha:0

here for 0.05 level and 7 degree of freedom crtiical value= -/+ 2.365

as test statistic for slope 5.316 is in critical region we reject null hypothesis

and conclude that  selling price is related to annual gross rents

d)

here null hypothesis: Ho: price and annual gross rents are indepednent

alternate hypothesis: Ha: there is a relation between  price and annual gross rents

for (1,7) degree of freedom in numerator and denominator at 0.05 level crtiical value =5.591

here test statisitc F =MS(regresion)/MS(residual)=(41976.4/1)/((52373.2-41976.4)/7)=28.262

as test statistic f is in critical region we reject null hypothesis

and conclude that  selling price is related to annual gross rents

e)

predicted selling price =(19+7.75*52.5) ($1000s) =425.875  ($1000s) or $425875