The 2nd image is a better fit, as the observed points are very
close to regression line as opposed to the 1st image.
For Graph I,
The regression line is given as:
We predict on the given data, using the given regression
estimate.
Using the above equation, we get the following table:
xi | yi | |||
1 | 2.6 | 1.19 | 1.41 | 1.9881 |
2.2 | 0.2 | 2.92 | -2.72 | 7.3984 |
3.4 | 7 | 4.65 | 2.35 | 5.5225 |
4.4 | 4.4 | 6.09 | -1.69 | 2.8561 |
5.6 | 8.2 | 7.81 | 0.39 | 0.1521 |
6.6 | 9.6 | 9.25 | 0.35 | 0.1225 |
Total | 18.0397 |
Thus, the SSE is 18.0397
The corrosponding degrees of freedom is 6-2 = 4.
The Standard Error of the Estimate =
For Graph II,
The regression line is given as:
We predict on the given data, using the given regression
estimate.
Using the above equation, we get the following table:
xi | yi | |||
1 | 1.6 | 1.67 | -0.07 | 0.0049 |
2.2 | 3.4 | 3.4 | 0 | 0 |
3.4 | 5.2 | 5.13 | 0.07 | 0.0049 |
4.4 | 6.4 | 6.57 | -0.17 | 0.0289 |
5.6 | 8.8 | 8.29 | 0.51 | 0.2601 |
6.6 | 9.4 | 9.73 | -0.33 | 0.1089 |
Total | 0.4077 |
Thus, the SSE is 0.4077
The corrosponding degrees of freedom is 6-2 = 4.
The Standard Error of the Estimate =
Thus, the Standard Error of estimate for Graph I is more
than that of Graph II.
Thus, the least square lie for Graph I fits the data less
efficiently than the least square line for Graph II fits its'
data.
The magnitude of the correlation cofficient for Graph i to be
less than the correlation coefficient for Graph II.
I hope this clarifies your doubt. If you're satisfied with the
solution, hit the Like button. For further
clarification, comment below. Thank You. :)
4. Comparing the fit of the regression lines for two sets of data Aa Aa E...
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