Question

Note: I will be going over the answers in class on January 24th. As such, late assignments will not be accepted. Assume you are interested in housing prices. You believe that the number of bedrooms will mpact the price of a home. Let bedroomi represent the number of bedrooms in home, and price, its price (in dollars). In this case the unit of observation is the home a) Write the population model of interest. b) Name two factors not accounted by the model that could affect the price a home, i.e. two factors that are in the error term. Briefly explain why you believe these factors would affect your dependent variable. b) Assume the following random sample from the Toronto housing market { (bedroom, price.) : İ-: 1, . . . , 4)) {(3, 50(XX)()), (2, 30()(00), (7, 100XX)(0), (4, 6(XX)(0)) Using the OLS estimator, calculate estimates of the intercept and the slope parameter. You are to do it by hand and show your work d) Interpret the estimate of interest e) Graph (to scale) the sample points, and the estimated line. Put the number of bedrooms on the horizontal axis and the price on the vertical axis.

Answer 1

a)

The population model of interest is,

Price = $\beta_0$ + $\beta_1$ Bedroom

b)

The other two factors that affect the price of the house is location (or distance from the city center) and age. Obviously, a new house will have the higher price than the old house for the same location and number of bedrooms.

If the house is near to the city center or downtown, the price will be higher.

c)

x = 3, 2, 7, 4

y = 500000, 300000, 1000000, 600000

$\sum x = 16$

$\sum y = 2400000$

$\sum x^2 = 78$

$\sum xy = 11500000$

$\bar{x} = \sum x / n = 16/4 = 4$

$\bar{y} = \sum y/ n = 2400000/4 = 600000$

$S_{xx} = \sum x^2 - \left ( \sum x \right )^2/n = 78 - 16^2 / 4 = 14$

$S_{xy} = \sum xy - \left ( \sum x \sum y \right )/n = 11500000 - (16*2400000) / 4 = 1900000$

Slope = Sxy / Sxx = 1900000 / 14 = 135714.3

Intercept = $\bar{y}$ - slope $\bar{x}$ = 600000 - 135714.3 * 4 = 57142.8

d)

Interpretation of Intercept - The price of the house with no bedrooms is 57142.8

Interpretation of slope - With increase in one bedroom in a house, the price of the house is increased by 135714.3.

e)

The graph of the sample points and estimated line is,

2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 Number of bedrooms