Question

Suppose you have been hired as a consultant by a local real estate company in central New Jersey. Your market research of real estate investments reveals the following sales figures for new homes of different prices over the past year.

Price (Thousands of $)	$150 - $169	$170 - $189	$190 - $209	$210 - $229	$230 - $249	$250 - $269	$270 - $289
Sales of New Homes This Year	126	103	82	75	82	40	20

If we simplify the situation by replacing each of the price ranges by a single price in the middle of the range, we get the following table:

Price (Thousands of $)	$160	$180	$200	$220	$240	$260	$280
Sales of New Homes This Year	126	103	82	75	82	40	20

We would like to use these data to construct a demand function for the real estate market. (Assume that a demand function gives demand y, measured here by annual sales, as a function of unit price, x.)

The data definitely suggest a straight line, more-or-less, and hence a linear relationship between sales and price.

(a) ( 4 points) Draw a straight line that best fits the data. Explain how do you choose the line? We would like the sales predicted by the best-fit line (predicted values) to be as close to the actual sales (observed values) as possible.

(b) (4 points) If the given points do not all lie on the best- fit line, how far away they are from lying on that line? Given regression equation is y = -0.7929x + 249.9. Mark the residuals on the graph.

Answer 1

(a).

So, the straight line that best fits the data is: Y = -15.857*X + 138.86

We chose this by using R-squared. This is with an R-squared of 0.9106 or 91.06%, which is a pretty good R-squared. This means 91.06% of variation in the dependent variable Y is being explained by the independent variable X from this data.

(b). Regression Output from Data Analysis Toolpack is shown below:

Residuals graph is shown below: