Is the Regression Line Useful for Predictions?
How do you know if the regression
line is useful in predicting the value of the dependent variable from
the value of the independent variable? You can determine that in various ways; we will discuss the most straightforward method below.
When you perform a regression analysis,
you select an Alpha value (normally 0.05). The software will include a Pvalue reported
in the analysis for the statistical test with the following hypotheses.
Statistical Hypotheses
Null Hypothesis: Slope of Regression line equals 0
Alternate Hypothesis: Slope of Regression Line does not equal 0
When a line has slope zero, the value of the independent variable has no effect on the value of the dependent variable. So, in order for a regression line to
have any prediction value, it must have a nonzero slope.
If the Pvalue is less than the Alpha value,
the null hypothesis is rejected; and so you assume the regression
line has a nonzero slope. You can use it to predict
the dependent variable using the independent variable.
Original work on this document was done
by Central Virginia Governor's School students Ashley Farmer, Josh Nelson
and Sara Throckmorton (Class of '98). Revisions were made by Ryan Malec, John Lewis
and Terri Kendrick (Class of '05)
Copyright © 2004 Central
Virginia Governor's School for Science and Technology Lynchburg,
VA
