complex linear regression equation example

One of the more provocative findings involved a multiple regression equation that was used to explain student performance. In response to the 1964 Civil Rights Act, the US government sponsored the 1966 Coleman Report, which was an ambitious effort to estimate the degree to which academic achievement is affected by student backgrounds and school resources. Gary Smith, in Essential Statistics, Regression, and Econometrics (Second Edition), 2015 The Coleman Report All of the techniques you learned earlier in this chapter can be used: predictions, residuals, R 2 and S e as measures of quality of the regression, testing of the coefficients, and so forth. More precisely, you have a linear relationship between Y and the pair of variables ( X, X 2) you are using to explain the nonlinear relationship between Y and X.Īt this point, you may simply compute the multiple regression of Y on the two variables X and X 2 (so that the number of variables rises to k = 2 while the number of cases, n, is unchanged). 26 This is still considered a linear relationship because the individual terms are added together. With these variables, the usual multiple regression equation, Y = a + b 1 X 1 + b 2 X 2, becomes the quadratic polynomial Y = a + b 1 X + b 2 X 2. Let us consider just the case of X with X 2. You are using polynomial regression when you predict Y using a single X variable together with some of its powers ( X 2, X 3, etc.).

You now have a multivariate data set with three variables: Y, X, and X 2.

The simplest choice is to introduce X 2, the square of the original X variable.

If the scatterplot of Y against X shows a curved relationship, you may be able to use multiple regression by first introducing a new X variable that is also curved with respect to X. Wagner, in Practical Business Statistics (Eighth Edition), 2022 Fitting a Curve With Polynomial RegressionĬonsider a nonlinear bivariate relationship.

Complex linear regression equation example