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The intuitive understanding is indeed as you suggest in the comment. If you think about the value of the slope for the regression as something that will change every time you draw a new sample (which …

Yes, some of the output has been removed. And while it would be much more straightforward to obtain the sample size with the information that was removed, there is another way to obtain the requested …

Here are my suggested answers: The use of $\eta^2 = R^2$ is not unreasonable. If you obtain the model without any $x$ variables (model lm.1) and the model with all of the variables containing an $x$ …

I have found myself Googling this question more than once: ¿What is the relationship between the standardized multiple regression coefficient (the standardized partial slope) and the corresponding se …

Let me use your $y$ and $x_3$ values. If you look only at the direct effect of $x_3$ on $y$, you will see a strong positive correlation. However, this ignores the other variables that may/may-not be i …

I am asking this from a pedagogic perspective:  ¿How do others explain (to their students or clients) the need to examine correlations between subsets of variables in multiple regression (MR) models? …

The long and short of the answer is: yes, the random and fixed effects are calculated/estimated at the same time. However, my sense is that you are not particularly interested in the mathematics behi …

When running a multiple regression model with interacting terms, you will want to include all of the main effects comprising those interactions in your model. Furthermore, if you have 3-way interacti …

Yes, this appears to be a typo. We can let residuals (from one model) be predictors in other models, but you are correct that the terminology, as presented in the problem, is incorrect. Furthermore, …

The general formula to transition between standardized coefficients, $\beta_1$, and unstandardized coefficients, $b_1$, is: $$\beta_1 = b_1 · \frac{s_1}{s_y}$$ where $s_1$ represents the standard devi …

You can assess if there is a statistically significant change in the coefficient of determination between the models with and without the two independent variables. For each model (#1 the smaller and …

Two things to keep in mind with MR analyses: First, the VIF cut-off of 10 is to flag extreme variance inflation. You have VIF values ≈2.5, which would result in $R^2 ≈ 0.6$...this means 60% of the var …

First, I am uncertain you have a multicollinearity problem, and you definitely do not have perfect multicollinearity. This would suggest that knowing one value, you know all the others. If I selecte …

My suggestion is that it could be either, but it depends on what you want to do with the interaction term. Said another way, the interaction term is going to change the slope for one of the variable …

With dummy coding, $\{0,1\}$, for each IV, the 4 cells would take on the values sad/low: $\mu$ sad/high: $\mu+\alpha$ happy/low: $\mu+\beta$ happy/high: $\mu + \alpha + \beta + \gamma$ So, the inter …