Question
In: Statistics and Probability
Given are five observations for two variables, and . 1 7 10 14 19 57 54...
Given are five observations for two variables, and .
| 1 | 7 | 10 | 14 | 19 | |
| 57 | 54 | 41 | 12 | 15 |
The estimated regression equation for these data is Y= 64.62-2.83x
a. Compute SSE, SST, SSR and .
| (to 2 decimals) | |
| (to 2 decimals) | |
| (to 2 decimals) |
b. Compute the coefficient of determination r2. Comment on the goodness of fit.
(to 3 decimals)
The least squares line provided a: good/bad fit ____%; of the variability in Y has been explained by the estimated regression equation (to 1 decimal).
c. Compute the sample correlation coefficient. Enter negative value as negative number.
(to 3 decimals)
Solutions
Expert Solution
| X | Y | X * Y |
 |
 |
SSE = 
|
SST = 
|
SSR = 
|
Residual | |
| 1 | 57 | 57 | 1 | 61.79443 | 22.9866 | 449.4400 | 675.7105 | -4.7944 | |
| 7 | 54 | 378 | 49 | 44.84154 | 83.8774 | 331.2400 | 81.7495 | 9.1585 | |
| 10 | 41 | 410 | 100 | 36.3651 | 21.4823 | 27.0400 | 0.3193 | 4.6349 | |
| 14 | 12 | 168 | 196 | 25.06317 | 170.6464 | 566.4400 | 115.2795 | -13.0632 | |
| 19 | 15 | 285 | 361 | 10.93576 | 16.5180 | 432.6400 | 618.2304 | 4.0642 | |
| Total | 51 | 179 | 1298 | 707 | 553.7303 | 315.5107 | 1806.8000 | 1491.2893 | 0.0000 |
SSE = 315.51
SST = 1806.80
SSR = 1491.29
Equation of regression line is 
b = -2.825
a =( 179 - ( -2.8255 * 51 ) ) / 5
a = 64.62
Equation of regression line becomes 
r = -0.909
Coefficient of Determination
Explained variation = 0.825* 100 = 82.5%
Unexplained variation = 1 - 0.825* 100 = 17.5%
orchestra answered 2 years agoRelated Solutions
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