Problem

Refer to Exercise.The accompanying table is similar to Table. It is used to make the preli...

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	—	—	—

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.