Do boys and girls make the same amount of progress?). Residuals are a measure of error in prediction so it may be worth using them to explore whether the model is more accurate for predicting the outcomes of some groups compared to others (e.g.
This provides the standardised residuals for each of your participants and can be analysed to answer certain research questions. You will also note that you have a new variable in your data set: ZRE_1 (you may want to re-label this so it is a bit more user friendly!). It also provides standardised versions of both of these summaries. The table below ( Figure 2.8.3) summarises the residuals and predicted values produced by the model.įigure 2.8.3: SPSS simple linear regression residuals output Finally the t-test in the second row tells us whether the ks2 variable is making a statistically significant contribution to the predictive power of the model - we can see that it is! Again this is more useful when performing a multiple linear regression. This becomes important when interpreting multiple explanatory variables so we'll come to this in the next module. Notice how there is also a standardised version of this second B-value which is labelled as Beta ( β ). This means that for every one standard mark increase in age 11 score (one tenth of a standard deviation) the model predicts an increase of 0.873 standard marks in age 14 score. In the Age 11 standard marks row the B column provides the gradient of the regression line which is the regression coefficient ( B). Basically in the (Constant) row the column marked B provides us with our intercept - this is where X = 0 (where the age 11 score is zero – which is the mean). This table can look a little confusing at first. The Coefficients table gives us the values for the regression line. Hopefully our model predicts the outcome more accurately than if we were just guessing the mean every time! Given the strength of the correlation it is not surprising that our model is statistically significant ( p <. Specifically it uses a ratio to compare how well our linear regression model predicts the outcome to how accurate simply using the mean of the outcome data as an estimate is. The ANOVA tells us whether our regression model explains a statistically significant proportion of the variance. In other words the success of a student at age 14 is strongly predicted by how successful they were at age 11. 785 suggests that 79% of the variance in age 14 score can be explained by the age 11 score. 886 suggests there is a strong positive relationship between age 11 and age 14 exam scores while r 2 =.
As we have already seen a coefficient of. The Model Summary provides the correlation coefficient and coefficient of determination (r 2) for the regression model. The next three tables ( Figure 2.8.2) get to the heart of the matter, examining your regression model statistically:įigure 2.8.2: SPSS Simple linear regression model output There is also a table entitled Variables Entered/Removed which we've not included on this page because it is not relevant! It becomes important for multiple linear regression, so we'll discuss it then. 0005) suggests there is a strong positive relationship between age 11 and age 14 exam scores. As we only have two variables there is only one correlation coefficient. More useful is the correlations table which provides a correlation matrix along with probability values for all variables. Extension B discusses issues of missing data. They are not exactly zero because certain participants were excluded from the analysis where they had data missing for either their age 11 or age 14 score. Because we are using standardised values you will notice that the mean is close to zero. The Descriptive Statistics simply provide the mean and standard deviation for both your explanatory and outcome variables. The first couple of tables ( Figure 2.8.1) provide the basics:įigure 2.8.1: Simple Linear regression descriptives and correlations output We've been given a quite a lot of output but don’t feel overwhelmed: picking out the important statistics and interpreting their meaning is much easier than it may appear at first (you can follow this on our video demonstration ). Interpreting Simple Linear Regression SPSS/PASW Output
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