Test of hypothesis about individual coefficients

We can make a test of hypothesis about any of the coefficients of model

Using the same procedure that we used to make a test of hypothesis about

for a simple regression model in previous chapter. The only difference is the degrees of freedom, which are equal to for a multiple regression.

In this case the value of the test statistic t for is calculated as

The value of is substituted from the null hypothesis.

If the regression errors are normally distributed and the standard regression assumptions hold, then the following hypothesis tests have significance level

1. To test either null hypothesis

or

against the alternative

the decision rule is

Reject if

2. To test either null hypothesis

or

against the alternative

the decision rule is

Reject if

3. To test null hypothesis

against the two sided alternative

the decision rule is

Reject if or

Remark: In most cases we are interested in the null hypothesis .

Example:

For example 1 of the section 4.5, using 1% significance level, can you conclude that the slope of the number of driving violations in regression model is 0 against the alternative that it is positive? Use the MINITAB solution given in Figure 4.1.

Solution:

is the number of driving violations committed during the past five years.

The portion of the solution is reproduced below

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