Interpretation of the Model summary table

The regression results comprise three tables in addition to the ‘Coefficients’ table, but we limit our interest to the ‘Model summary’ table, which provides information about the regression line’s ability to account for the total variation in the dependent variable. Figure 6 demonstrates that the observed y-values are highly dispersed around the regression line. Thus, as regression analysts often put it, the regression model only ‘explains’ a limited proportion of the dependent variable’s total variation. The dependent variable’s total variation can be measured by its variance. If the regression line is not completely horizontal (i.e. if the b coefficient is different from 0), then some of the total variance is accounted for by the regression line. This part of the variance is measured as the sum of the squared differences between the respondents’ predicted dependent variable values and the overall mean divided by the number of respondents. By dividing this explained variance by the total variance of the dependent variable, we arrive at the proportion of the total variance that is accounted for by the regression equation. This proportion varies between 0 and 1 and is symbolised by R2 (R Square). As can be seen from Table 2, the value of our R2 is 0.131, which means that 13.1 percent of the total variance in education length has been ‘explained’. Not very impressive, but not bad either compared with the R2 values one tends to get in analyses of social survey data. The R is the square root of R2. The Adjusted R2 will be discussed later.

Table 2. SPSS output: Simple linear regression goodness of fit

Exercises

  1. Perform the same regression analysis as in the example presented above on data from the Polish (or another county’s) ESS sample.
  2. Perform a regression analysis with ‘How happy are you’ as the dependent variable and ‘Subjective general health’ as the independent variable. (These variables are not metric, but they can, at least as an exercise, still be used in OLS regression.) Use data from a country of your own choice. What do the results tell you?
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