1. [Simple linear regression] The XXX Real Estimate Research Center collected data on the homes sold in a city during 2018. The selling prices y and living areas in square feet x of 20 homes are given below.
Home Price Area
1 $ 860,000 870
2 $ 860,000 840
3 $ 920,000 1032
4 $ 925,000 1168
5 $ 935,000 1100
6 $ 940,000 1430
7 $ 1,040,000 1520
8 $ 1,045,000 1468
9 $ 1,099,000 1160
10 $ 1,119,000 1800
11 $ 1,189,000 2052
12 $ 1,250,000 1590
13 $ 1,306,000 1600
14 $ 1,398,750 2044
15 $ 1,444,000 1916
16 $ 1,480,000 2024
17 $ 1,560,000 1840
18 $ 1,519,000 1684
19 $ 1,595,000 1760
20 $ 1,630,000 2260
a. What is the average square footage and selling price of the homes in the sample?
b. Construct a scatter plot and find the correlation coefficient. Interpret.
c. Determine the least squares regression equation. Give a practical interpretation of the parameter estimates and s.
d. Test whether there is a significant linear relationship between selling price and area. Use α = .05.
e. Interpret the coefficient of determination, r².