The table shows the total square footage (in billions) of retailing space at shopping centers and their sales (in billions of dollars) for 10 years. The equation of the regression line is
ModifyingAbove y with caret equals 605.666 x minus 2189.023y=605.666x−2189.023.
Complete parts a and b.
|
Total Square Footage, x |
5.15.1 |
5.25.2 |
5.15.1 |
5.45.4 |
5.55.5 |
5.75.7 |
5.75.7 |
5.95.9 |
5.95.9 |
6.16.1 |
|
|---|---|---|---|---|---|---|---|---|---|---|---|
|
Sales, y |
881.6881.6 |
940.1940.1 |
981.4981.4 |
1050.21050.2 |
1121.81121.8 |
1200.71200.7 |
1294.31294.3 |
1339.11339.1 |
1438.91438.9 |
1536.71536.7 |
|
(a) Find the coefficient of determination and interpret the result.
| S.No | X | Y | (x-x̅)2 | (y-y̅)2 | (x-x̅)(y-y̅) |
| 1 | 5.1 | 881.6 | 0.2116 | 88137.73 | 136.5648 |
| 2 | 5.2 | 940.1 | 0.1296 | 56825.02 | 85.8168 |
| 3 | 5.1 | 981.4 | 0.2116 | 38840.53 | 90.6568 |
| 4 | 5.4 | 1050.2 | 0.0256 | 16455.76 | 20.5248 |
| 5 | 5.5 | 1121.8 | 0.0036 | 3212.62 | 3.4008 |
| 6 | 5.7 | 1200.7 | 0.0196 | 493.73 | 3.1108 |
| 7 | 5.7 | 1294.3 | 0.0196 | 13414.27 | 16.2148 |
| 8 | 5.9 | 1339.1 | 0.1156 | 25798.78 | 54.6108 |
| 9 | 5.9 | 1438.9 | 0.1156 | 67818.58 | 88.5428 |
| 10 | 6.1 | 1536.7 | 0.2916 | 128321.57 | 193.4388 |
| Total | 55.6 | 11784.8 | 1.1440 | 439318.60 | 692.8820 |
| Mean | 5.560 | 1178.48 | SSX | SSY | SXY |
| SST=Syy= | 439,318.5960 | |
| SSE =Syy-(Sxy)2/Sxx= | 19,663.4684 | |
| SSR =(Sxy)2/Sxx = | 419,655.1276 | |
| Coeffficient of determination R^2 =SSR/SST= | 0.955 | ||
95.5% of variation in sales can be explained by variation in Total Square Footage
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