Question

A regression analysis is conducted with 9 observations.

**a.** What is the df value for inference about the
slope β?

**b.** Which two t test statistic values would give
a P-value of 0.01 for testing H0: β=0 against Ha: β ≠0?

**c.** Which t-score would you multiply the
standard error by in order to find the margin of error for a

99% confidence interval for β?

Answer #1

A regression analysis is conducted with 9 observations.

n=9

a) degree of freedom value for inference about the slope β is

df=n-2

df=9-2=7

Regression analysis is conducted with 9 observations. The degrees of freedom are 7.

b)

For testing H0: β=0 against Ha: β ≠0, the test statistic equals:

Where *b* is the sample slope and *se* denotes its
standard error

Using t critical table for a two-tailed test with alpha = 0.01 and df (7), we get

t- critical = -**3.499425** and
**3.499425**

Therefore, t test statistic = -**3.499425**,
**3.499425**

**c)**

(c) From part (b), we have calculated t critical value = 3.499

So, we will multiply the standard error by 3.499 to get the margin of error

t critical = 3.499

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