Refer to Exercise.
The accompanying table is similar to Table. It is used to make the preliminary computations for finding the least squares line for the given pairs of x and y values.
a. Complete the table.
b. Find SSxy.
c. Find SSxx.
d. Find
e. Find
f. Find .
g. Find the least squares line.
| xi | yi | xi2 | xi yi |
| 7 | 2 | — | — |
| 4 | 4 | — | — |
| 6 | 2 | — | — |
| 2 | 5 | — | — |
| 1 | 7 | — | — |
| 1 | 6 | — | — |
| 3 | 5 | — | — |
Totals |
After the least squares line has been obtained, the following table (which is similar to Table
Comparing Observed and Predicted Values for the Least Squares Prediction Equation | ||||
x | y | ŷ = -.1 + .7x | (y – ŷ) | (y – ŷ)2 |
1 | 1 | .6 | (1-.6) = .4 | .16 |
2 | 1 | 1.3 | (1-1.3) = - .3 | .09 |
3 | 2 | 2.0 | (2-2.0) = 0 | .00 |
4 | 2 | 2.7 | (2-2.7) = - .7 | .49 |
5 | 4 | 3.4 | (4-3.4) = .6 | .36 |
|
|
| Sum of errors = 0 | SSE = 1.10 |
)
x | y | ŷ | (y – ŷ) | (y – ŷ)2 |
7 | 2 | — | — | — |
4 | 4 | — | — | — |
6 | 2 | — | — | — |
2 | 5 | — | — | — |
1 | 7 | — | — | — |
1 | 6 | — | — | — |
3 | 5 | — | — | — |
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|
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can be used (1) to compare the observed and the predicted values of y and (2) to compute SSE.
a. Complete the table.
b. Plot the least squares line on a scatterplot of the data. Plot the following line on the same graph:
c. Show that SSE is larger for the line in part b than it is for the least squares line.
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