Final answer:
The test statistic for the slope of a least squares regression line is calculated by dividing the difference between the sample slope and the hypothesized slope by the standard error of the slope. This is commonly used to test the significance of the regression slope.
Step-by-step explanation:
The formula for the test statistic for the slope of a least squares regression line is given by:
t = (b - β) / (sb)
where b represents the calculated slope of the least squares regression line from sample data, β (beta) is the hypothesized slope (often 0 if testing whether there is a relationship), and sb is the standard error of the slope.
To find the test statistic for the slope of a least squares regression line:
- Calculate the slope b of the regression line.
- Determine the standard error of the slope (sb), which can be calculated using the standard deviation of the residuals s and the sum of the squares of the x-values.
- Formulate the test statistic using the observed slope b, hypothesized slope β, and standard error of the slope (sb).
In the context of the third exam/final exam example, if we want to test the significance of the slope (b = 4.83) estimated from the sample, we would compute the test statistic using the aforementioned formula where the hypothesized slope β is often 0 (zero).