| Time | Chapter |
|---|---|
| 16:20 | Welcome to block 3We are returning to our old friend, our first friend in SSR, the regression module. In block 3 we're not going to be looking at categorical predictors, but at continuous predictors, so the theme of block 3 is life is also continuous. |
| 21:22 | Multiple regressionWe are still in the business of trying to predict an outcome variable as best as possible by looking at one or more predictor variables. With continuous predictors, every continuous predictor gets a single regression weight. |
| 23:58 | Outcome vs model predictionThese scatter plots between prediction and outcome visualize exactly the proportion of explained variance, which we denote with r-squared. The higher the r-squared, the better the model predicted. |
| 27:26 | Plotting the data (applet)Always plot your data, because plots are a great way already to assess various assumptions. We predict how well an album sells from two predictor variables, advertisement budget and airplay, and a matrix scatter plot gives a first idea of how they are associated. |
| 32:45 | Explained variance with one predictor (applet)The explained variance is an effect size, a proportion between zero and one. An F statistic is a test statistic for hypothesis testing, and you can turn your R-squared into an F statistic to test whether the increase in explained variance is significant. |
| 39:32 | Two predictors and an interaction (applet)The moment your predictors are associated, the unique contribution of a predictor is harder to quantify. Now we incorporate both advertisement budget and airplay in predicting album sales, and we can even include the interaction effect. |
| 42:52 | Testing the regression coefficientsJust as with regression with a single predictor, we can still test whether the regression coefficients are equal to 0 or not. If a coefficient equals 0, it has no predictive value for predicting the outcome variable. |
| 47:12 | AssumptionsWe are still working with the linear model, and if its assumptions are violated, you cannot rely so much anymore on your inferential statistics. Homoscedasticity, the regression equivalent of equal variances, becomes more and more important as you add more predictors to your model. |
| 53:10 | Multicollinearity and the VIFMulticollinearity means very strongly associated predictor variables, and if all your predictors look the same, you cannot attribute the explained variance to one specific variable anymore. You assess it with the VIF, and only for the main effects, not for the interaction effect. |
| 59:01 | The bootstrap as a robust alternativeIf you have one of these assumption problems, you can also choose to use what's called the bootstrap. It is a way to have more robust confidence intervals when you have such assumption violations. |
| 59:54 | The album sales exampleThe actual example predicts album sales from two predictor variables, airplay and advertisement budget. We have 200 observations, so the normality assumption is not going to be so important anymore. |
| 1:01:30 | Break |
| 1:12:47 | From a regression line to a regression planeWith one predictor, a line gives the predictions of the model. With two predictors, we visualize our model predictions with a plane, chosen in such a way that it's as close to all the points as possible. |
| 1:18:44 | Predicted values from the modelBased on the regression weights, we can calculate the predictions that our model makes. You can also plug new values of airplay and advertisement budget into the regression formula to make predictions for new data. |
| 1:21:16 | How far are we off?We take the difference between observed and predicted, and that is our model error, our model residuals. R-squared is the squared correlation between observed and predicted, but you can also see it as the model sums of squares divided by the total sums of squares. |
| 1:28:55 | Hierarchical regressionHierarchical regression allows you to get a better idea of an individual predictor's contribution, where the next model builds upon the previous one. We look at the R-squared change, and this R-squared change also has a corresponding F statistic that you can use to do hypothesis testing. |
| 1:31:34 | Multiple regression in JASPThe model summary table tells something about each model as a whole, and the coefficients table lists the regression coefficients corresponding to each predictor. On open questions, always be more specific about what p-value you refer to. |
| 1:41:45 | Checking the assumptions in JASPFor influential cases you tick Case-wise diagnostics, and a Cook's distance close to one tells you that you have an influential case. The residuals versus predicted plot assesses homoscedasticity, and the tolerance and VIF box checks multicollinearity. |
| 1:48:25 | Hierarchical regression in JASPIn the Model tab we make multiple models, and we control for a variable by adding it to all the models. Adding airplay gives a significant increase in R-squared, but adding the interaction effect gives barely any increase. |
| 1:57:32 | RecapWe've seen how to say something about overall model performance with the r-squared, and how to make more specific model comparisons where the only difference between two models is a single predictor. Tomorrow is mediation analysis, explicitly modeling dependence between predictors. |
21. Multiple regression
Summary and chapters of the recording
27 October 2026 · Recording · Slides · Handout
We open block 3 (life is continuous) with multiple regression, predicting album sales from two continuous predictors, advertisement budget and airplay. In the applet we see how every predictor we add changes the model predictions and the explained variance (R²), and how the regression coefficients are tested. Then we go through the assumptions, with extra attention to multicollinearity and the VIF, and meet the bootstrap as a robust alternative. After the break we picture the model as a plane in three dimensions, compute its predictions and errors, and use hierarchical regression to isolate what a single predictor adds (the R² change). We finish with the full analysis in JASP, assumption checks included.
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