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If the relationship you wish to examine is looking at the product as its own stand-alone concept (e.g., area as opposed to the two separate lengths), then you have $z=x_1·x_2$ and you can simply run a regression … That is to say, run a regression to predict $\ln(y)$ from both $\ln(x_1 · x_2) = \ln(x_1) + \ln(x_2)$. …

I would suggest using Structural Equation Modeling (SEM) to address this problem. In brief, you are proposing a latent variable, welfare index, which is directly influencing 4 manifest (measured or ob …

You have calculated the semi-partial correlation for ln(wages) and education controlling for gender—though you have done so using a follow-up regression instead of just calculating the correlation.  … Again, you used a regression approach (instead of correlation), but the interpretations would generally be the same. Addendum #1 I wouldn't post an answer with an addendum usually.  …

When you run the regression model in Excel, be sure to select only that part of the data that you want to use as the training data set.  … You can then generate the regression coefficients for the model.  Next, you will need to calculate the estimated values for the rest of the data (the test data set) manually.  …

If you take the regression for each cloud separately, you will obtain a positive slope. … However, if you combine the data sets into one (and ignore the grouping structure), then the aggregate regression will have a negative slope. …

As for APA format, the best strategy is to Google the title of a common APA journal (say Journal of Educational Psychology) and "logistic regression". …

If you decide to model the transformation of a variable, then you can simply undo the transformation once you have the model. For example, if you model $z = y^2$ as $$z = \beta_0 + \beta_1 x_1 + \bet …

Simply put, with regards to dummy coding for categorical variables in multiple regression models, this simply is not the case.  …

It sounds as though you might be exploring a question of moderation. That is to say, ¿does the relationship between a dependent variable and the predictors change for different groups? As such, the t …

Here is the information for a null hypothesis statistical test (NHST) a single-sample test comparing 2 correlations (this comes from Kleinbaum, Kupper, Nizam & Rosenberg, 5th ed.). If you wish to test …

Before jumping to regression, let's think about a simpler setting: a two sample $t$-test. Here, you have two groups (sample sizes $n_1$ and $n_2$) and each has a mean. … The regression formula would be $$y = a + b_1 · X_1 + b_2 · X_2 + b_3 · X_3 + b_4 · X_4 $$ But, the same rationale holds. …

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 issue is with the categorical predictors in a multiple regression (MR) setting.  … In the regression model, you would have an intercept and a slope for this variable, female, and maybe other variables.  …

First, I do not know if there is a comparable set of packages or functions like can do automated model comparison testing (similar to step() or regsubsets()). Second, if you are comparing changes in …

We can solve polynomial regression using linear regression because we can treat the higher ordered powers as separate independent variables in the regression model (thus, the model parameters can be estimated …