Regression Equation

Home > Statistics Every Writer Should Know > The Stats Board > Discusssion

Regression Equation
Message posted by Sheena on July 23, 2000 at 12:00 AM (ET)

I need a real good example to demonstrate of the practical application of the regression equation.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Regression Equation
Message posted by Phil on July 23, 2000 at 12:00 AM (ET)

Suppose you knew the GPA and SAT scores for a lot of students. You could treat GPA as the independent variable (x) and use the data to develop the regression equation to predict SAT score (y). If there is a high degree of correlation between GPA and SAT scores, then the model can be used to predict SAT scores given the GPA. The model would be y = a + bx where "a" and "b" are parameters estimated from the data. A high correlation coefficient (r) means the model is a good predictor of the dependent variable (y).

Note: Just because you get good correlation does not mean that there is a "cause & effect" relationship. You have to have more than just raw data to determine that. Good models also "fit" the data well. You determine that by analyzing "residuals". (probably more than you wanted to know). The example given was for a linear model. Transformations exist to fit non-linear models also.

Your $5 contribution helps cover part the $500 annual cost of keeping this site online.