Learning the mechanics. Consider the 10 data points shown in the table
|
x
|
30
|
50
|
70
|
90
|
100
|
120
|
140
|
160
|
180
|
200
|
|
y
|
4
|
10
|
15
|
21
|
21
|
22
|
29
|
34
|
39
|
41
|
(a) Fit a straight-line model through the origin; i.e., fit E(y) = β1x.
(b) Calculate SSE, s2, and s.
(c) Do the data provide sufficient evidence to indicate that x and y are positively linearly related?
(d) Construct a 95% confidence interval for β1.
(e) Construct a 95% confidence interval for E(y) when x = 125.
(f) Construct a 95% prediction interval for y when x = 125.