Question

(Q,111) Use the following pairs of observations to construct an​ 80% and a​ 98% confidence interval...

(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: -----------?

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)

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