In: Statistics and Probability
Determine the linear correlation coefficient between square footage and asking price.
Square Footage, x Selling Price ($000s), y
2209 380.7
3323 396
1105 186.3
1953 334.5
3225 639.7
2741 365.7
3987 608
2147 367
2536 413.6
1632 286.2
1749 265.3
3882 700.2
r= ?
Solution:
Correlation coefficient can be calculated as
n*Summation(XY) -
Summation(X)*Summation(Y)/sqrt(n*summation(X^2)-(Summation(X))^2)(n*Summation(Y)^2
- (Summation(Y))^2)) =
X |
Y |
X^2 |
Y^2 |
XY |
2209 |
380.7 |
4879681 |
144932.49 |
840966.3 |
3323 |
396 |
11042329 |
156816 |
1315908 |
1105 |
186.3 |
1221025 |
34707.69 |
205861.5 |
1953 |
334.5 |
3814209 |
111890.25 |
653278.5 |
3225 |
639.7 |
10400625 |
409216.09 |
2063032.5 |
2741 |
365.7 |
7513081 |
133736.49 |
1002383.7 |
3987 |
608 |
15896169 |
369664 |
2424096 |
2147 |
367 |
4609609 |
134689 |
787949 |
2536 |
413.6 |
6431296 |
171064.96 |
1048889.6 |
1632 |
286.2 |
2663424 |
81910.44 |
467078.4 |
1749 |
265.3 |
3059001 |
70384.09 |
464009.7 |
3882 |
700.2 |
15069924 |
490280.04 |
2718176.4 |
30489 |
4943.2 |
86600373 |
2309291.54 |
13991629.6 |
Correlation = (12*13991629.6) - (30489*4943.2) / sqrt((12*86600373
- 30489*30489)(12*2309291.54 - 4943.2*4943.2)) =
17186330.4/sqrt(109625355*3276272.24) = 0.9069