Refer to Exercises.
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 |
And
Consider the following pairs of measurements, saved in the LM9_17 file:
x | 5 | 3 | -1 | 2 | 7 | 6 | 4 |
y | 4 | 3 | 0 | 1 | 8 | 5 | 3 |
a. Construct a scatterplot of these data.
b. What does the scatterplot suggest about the relationship between x and y ?
c. Given that SSxx = 43.4286, SSxy = 39.8571, = 3.4286, and = 3.7143, calculate the least squares estimates of β0 and β1
d. Plot the least squares line on your scatterplot. Does the line appear to fit the data well? Explain.
e. Interpret the y -intercept and slope of the least squares line. Over what range of x are these interpretations meaningful?
Calculate SSE, s2, and s for the least squares lines obtained in those exercises. Interpret the standard errors of the regression model for each.
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