In this article
A Linear Regression run gives a set of tables that present the resulting data .
Figure 1 - Example of the results of a linear regression run
The data presented in the tables is as follows:
- Model Summary - This table contains information about how good the regression model fits the data.
- R Square - the Coefficient of determination. This is the proportion of variability in the data set that is accounted for by the linear regression model. The value is between 0 and 1, where 1 is a perfect match between the model and the data.
- Adjusted R Square - This is a modification of R Square adjusted for the sample size and the number of independent variables.
- Std Error of the Estimate - This is a measure of the accuracy of predictions when using the linear regression model on arbitrary data.
- ANOVA - This table contains the analysis of variance (ANOVA), which consists of calculations that provide information about levels of variability within a regression model and form a basis for tests of significance.
- Sum of Squares - This column contains the sum of squares for the estimates based on the regression model (SSR), the residuals (SSE) and the total data (SST). SST = SSR + SSE.
- df - Degrees of freedom. For the regression model this is equal to the number of independent variables (p), for the total data this is equal to the number of data observations minus one (n - 1), and for the residuals this is equal to the number of cases minus the number of independent variables minus one (n - p - 1).
- Mean Square - This is the sum of squares divided by the corresponding number of degrees of freedom.
- F - The F-value is the basis for the hypothesis test of every calculated coefficient being 0 (null hypothesis) versus at least one of the calculated coefficients being different from 0 (alternative hypothesis). Large F-values provides evidence against the null hypothesis. The value is calculated as the Mean Square for the regression model divided by the Mean Square for the residuals.
- Sig. - This is the significance level for the F-value, based on the F(p, n - p - 1) distribution. Small values for this gives strong evidence for the alternative hypothesis.
- Coefficients - This table contains the calculated coefficients for the linear regression model, and an analysis of the significance level for each coefficient. The first row contains the constant term, signifying the base level for the dependent variable.
- Unstandardized coefficients - This column contains the calculated coefficients for the linear regression model (based on least squares estimation), and the standard error for the estimates.
- Standardized coefficients - These coefficients are calculated based on standardized independent variables (variance standardized to 1). These standardized coefficients are used to predict which of the independent variables have the greater effect on the dependent variable, when the independent variables may have different units of measurement.
- t - The t-value is the basis for the hypothesis test of the calculated computed coefficient being 0 (null hypothesis) versus it being different from 0 (alternative hypothesis). Large t-values provide evidence against the null hypothesis. The value is calculated as the estimate of the unstandardized coefficient divided by the corresponding standard error.
- Sig. - This is the significance level for the t-value, based on the t-distribution with n - p - 1 degrees of freedom. Small values for this give strong evidence for the alternative hypothesis.