Question: Recall our analysis of the data on Condo sales, with an asking price of $169,000, interior space of 1040 square feet, five rooms, two bedrooms and one bath.

I used the MS Excel ‘Data/Filter’ to select a subset of the 456 records to include only those located in Mid-Cambridge and with interior space of between 800 and 2000 Ft², selling price between $100,000 and $200,000, and date of closing since July 15, 1992. This ‘Filter’ data set yielded only 32 observations for a preliminary plot. I then noticed 3 of the sales were extreme ‘outliers’ and removed them, leaving 29 useful observations. I then ran a simple linear regression of selling price predicted by interior space in Ft² to see whether this might be useful in determining if this asking price of $169,000 is “fair”. The “X-Y Plot” and Regression Statistics for these 29 observations are shown below.

Case data with Filters Filtered data: Area= MidCamb; CloseDate >7/15/92; Sale Price = $100K to $200K; SqFt= 800 to 2000 then delete 3 'outlier' observations
Regression Statistics
R Square	0.58
Observations	29
	Coefficients	Std Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-20863	29289	-0.71	0.4824	-80958	39232
SqrFt	177	29.1	6.08	0.000002	117	237

(a) How useful is this overall relationship, in terms of explaining the variability in Sale Price for these 29 condo’s in the filtered data set?

(b) What is its 90% confidence range for this estimate of the coefficient of $177 per square foot to help estimate the Sale Price? What is the probability it might even be less than zero, and therefore meaningless? [no calculations, all these have been done by Excel in the above display]

(c) Calculate the estimated ‘fair selling price’ for the condo Reyem Affiar is considering with 1040 square feet of space in this Mid-Cambridge area?