Question

(Q,111)

Use the following pairs of observations to construct an​ 80% and a​ 98% confidence interval for beta 1β1.

x          y

5          4

0          1

3          3

2          2

4          3

6          8

1          2

The​ 80% confidence interval is: -----------?

The​ 98% confidence interval is: -----------?

Answer 1

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 0.5 + 0.92857143 x
Sample size: 7
R (correlation coefficient) = 0.87645982
R-sq = 0.76818182
Estimate of error standard deviation: 1.2071217

Parameter estimates:

Parameter	Estimate	Std. Err.	DF	80% L. Limit	80% U. Limit
Intercept	0.5	0.82251481	5	-0.71393648	1.7139365
Slope	0.92857143	0.22812456	5	0.59188603	1.2652568

Parameter estimates:

Parameter	Estimate	Std. Err.	DF	98% L. Limit	98% U. Limit
Intercept	0.5	0.82251481	5	-2.2677048	3.2677048
Slope	0.92857143	0.22812456	5	0.16094823	1.6961946

Hence,

80% confidence interval: (0.592, 1.265)

98% confidence interval: (0.161, 1.696)