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)

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