Question

1.   There are two major websites that use mathematical models to predict the price of houses based on things like # of bedrooms, square feet, location, what similar houses sell for, all kinds of variables. You’re going to select a sample of houses and see which website predicts better.

a.   Decide on a location for your sample. Anywhere in the US works. Write the location here.
Fresno, CA

b.   Go to www.zillow.com and check “Recently Sold.” Randomly select at least 15 homes that have recently sold and record the Zestimate and selling price. Then go to redfin.com and find the Redfin Estimate for the same 15 houses. (Note that on both websites you can filter houses by if they are for sale or if they have sold.)

Home#1	Zestimate	Redfin Estimate	Sale Price
1	367,846	252,554	335,000
2	314,085	293,763	295,000
3	327,343	337,693	350,000
4	270,548	259,655	260,000
5	153,270	146,012	142,500
6	133,920	118,487	106,500
7	230,040	234,905	225,000
8	1,429,459	1,259,453	1.35M
9	135,240	130,020	134,000
10	210,515	214,877	212,000
11	344,369	308,848	342,000
12	279,008	265,839	270,000
13	406,836	265,566	395,000
14	301,213	286,458	277,500
15	156,575	198,387	190,000

c.   Create a scatterplot. Put the Zestimate on the horizontal axis and the Sale Price on the vertical axis. Be sure your plot has axis labels and a title. Paste the plots here. (You can copy-paste from Excel or Google Docs, or a similar tool. Hand-drawn is only acceptable if it’s done with very high precision. Calculator screens won’t look good at all for this.)
d.   Do the same with the Redfin estimate and the Sale Price.
e.   Based on the scatterplots, does it look like one of the two sites is better, or are they about the same? Answer in complete sentences.
f.   Are there any outliers in either plot? If so, identify them. Answer in complete sentences.
g.   Calculate the correlation coefficient for each plot. Put the results in a sentence or two and explain what these values mean, in relation to the plots.
h.   Pick one of the two plots. Are the conditions for linear regression met? Explain in 1 – 5 sentences.
i.   Find the equation of the least-squares regression line.
j.   Interpret the slope of the line in a sentence.
k.   Interpret the intercept of the line in a sentence.

Answer 1

c.

d.

e. They are both the same

f. Yes, there is an outlier in both the plots. The outlier is home 8 which has zestimate as 1429459,redfin estimate as 1259453 and sales is 1.35M

g. Correlation coefficient for Zestimate and sales is 0.9984 .

Correlation coefficient for Redfin estimate and sales is 0.9916 .

h. Yes, the plot of zestimate - sales satisfies the condition of linear regression as they form a straight line i.e., they are normally distributed along the regression line. Also the correlation coefficient supports the linear regression.

i. The regression equation is y = 0.9392 x + 8793.5 where y is sales and x is zestimate.

j. The slope is 0.9392 which means that a unit increase in zestimate there is 0.9392 increase in sales.

k. The intercept is 8793.5, the expected mean value of Y when X is o.