Question

A local realtor wishes to study the relationship between selling price (in $) and house size
(in square feet). A sample of 10 homes is selected at random. The data is given below:

PRICE	HOUSESIZE
100000	1600
107000	1750
121000	1900
124000	2150
132000	2400
140000	2300
144000	2400
158000	2700
170000	3000
182000	2900

a) Find the regression equation relating Price to Square Footage.

b) Calculate the correlation coefficient, accurate to three decimal places  

c) Test the significance of the correlation coefficient with a 0.05 level of significance.
Include definition of hypotheses, test statistic, p-value or critical value, decision about Ho, and conclusion.

d)  What is the best estimate for a 2000 sq. ft home?

Answer 1

ΣΑ, Zy; Let X denote the size and y denote the price then 23100 1378000 I = 2310 ✓ = 137800 n 10 n 10 Xx? 55365000 Σ» 196214000000 = 5536500 1962 1400000 10 n 10 n :: V(X) = -(7)? = 200400 V (Y) = (T)° = 632560000 n n Xxy COV(X,Y)= - XV 3292550000 -318318000 = 10937000 10 n 1 = The estimated regression equation is û = a + bx where COV(X,Y) 10937000 = 54.5758 and V(X) 200400 à= 5 - 6x = 137800 - (54.5758 * 2310) = 11729.79 Therefore û = 11729.79 +54.5758x b. The correlation coefficient is COV (X,Y) 10937000 0.9714 V(X)/(Y) 1200400 * 632560000 The null hypothesis to be tested is Ho: P = 0 and the alternative is H:p0 The test statistic is run - 2 0.971476 t = 11.571 V1-72 V1 -0.9714? From t-table with 8 degrees of freedom the critical values are -2.306 and 2.306 The p-value is P(t> 11.571) = 0.0000028 So the conclusion is reject the null hypothesis. i.e. there exist a significance correlation between the variables d. When x=2000 the estimate ofy is û =11729.79 + 54.5758* 2000 = 120881.5