Question

Suppose you have the following data.

Year	# New Homes Sold (1000s)	Conventional Mortgage Interest Rate
1995	667	7.93
1996	757	7.81
1997	804	7.6
1998	886	6.94
1999	880	7.44

Let H be the number of new homes sold and let M be the conventional mortgage interest rate.

1. Find the sample mean of H and the sample mean of M.

2. Find the sample variance of H and the sample variance of M. Additionally, calculate the sample covariance of H and M.

3. Calculate the linear regression where H is the independent variable and M is the dependent variable.

4. Based on the linear regression from part b what variable affects the other and what type of numerical effect does it have?

Answer 1

Sample mean = sum of all units / Total number of units

Sample mean of H = 3994/5 = 798.8

Sample mean of M = 37.72/5= 7.544

The formula for Sample variance is

Where X is the value of the unit

Xbar is the mean

N is the sample size

Sample variance of H = 33342.8/ (5-1) = 8335.7

Sample variance of M = 0.5959/4 = 0.148975

Sample covariance

Covariance = -120.1992/4 = 30.0498

H is independent

and M is dependent

The Line will look like this

M = a +bH

b =

= -120.1992/ 33342.8= -0,0036

a = Mbar - bHbar

= 7.544 - (-0.0036)* 798.8

= 10.41

The linear regression is

M = 10.41 -0.0036H

Based on the regression equation a 1 unit change in H produces a negative effect of 0.0036 in M.

It has a negative effect.