The Coefficient of Correlation between square footage and listing price
|
X
|
Y
|
X⋅Y
|
X⋅X
|
Y⋅Y
|
|
1400000
|
0
|
0
|
1960000000000
|
0
|
|
1200000
|
1000
|
1200000000
|
1440000000000
|
1000000
|
|
1000000
|
2000
|
2000000000
|
1000000000000
|
4000000
|
|
800000
|
3000
|
2400000000
|
640000000000
|
9000000
|
|
600000
|
4000
|
2400000000
|
360000000000
|
16000000
|
|
400000
|
5000
|
2000000000
|
160000000000
|
25000000
|
|
200000
|
6000
|
1200000000
|
40000000000
|
36000000
|
|
0
|
7000
|
0
|
0
|
49000000
|
Sum of every column:
∑X=5600000 , ∑Y=28000 , ∑X⋅Y=11200000000 , ∑X2=5600000000000 , ∑Y2=140000000
Formula used
r r = n⋅∑XY−∑X⋅∑Y[n∑X2−(∑X)2]⋅[n∑Y2−(∑Y)2]−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√= 8⋅11200000000−5600000⋅28000[8⋅5600000000000−56000002]⋅[8⋅140000000−280002]−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−√≈−1
The coefficient of correlation is r = -1
Q1. Does the Coefficient of Correlation seem consistent with the information above? Why or why not?
Q2. What proportion of the variation in listing price is determined by variation in the square footage? What proportion of the variation in listing price is due to other factors?