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### Will an OLS estimator for a regressor differ between a single linear regression and a multiple linear regression? [duplicate]

Thought question that I am having a difficult time formulating mathematically. Knowing that $y = \beta_0 + \beta_1X_1 +\beta_2X_2 + \varepsilon$, where $X_1$ and $X_2$ are non-random and $\beta_2$ ...
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### How can adding a 2nd IV make the 1st IV significant?

I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out. I have a least squares regression model, with one independent variable and one ...
24k views

### How to visualize what canonical correlation analysis does (in comparison to what principal component analysis does)?

Canonical correlation analysis (CCA) is a technique related to principal component analysis (PCA). While it is easy to teach PCA or linear regression using a scatter plot (see a few thousand examples ...
44k views

### X and Y are not correlated, but X is significant predictor of Y in multiple regression. What does it mean?

X and Y are not correlated (-.01); however, when I place X in a multiple regression predicting Y, alongside three (A, B, C) other (related) variables, X and two other variables (A, B) are significant ...
73k views

### What is the expected correlation between residual and the dependent variable?

In multiple linear regression, I can understand the correlations between residual and predictors are zero, but what is the expected correlation between residual and the criterion variable? Should it ...
48k views

### Multiple regression or partial correlation coefficient? And relations between the two

I don't even know if this question makes sense, but what is the difference between multiple regression and partial correlation (apart from the obvious differences between correlation and regression, ...
19k views

### Importance of predictors in multiple regression: Partial $R^2$ vs. standardized coefficients

I am wondering what the exact relationship between partial $R^2$ and coefficients in a linear model is and whether I should use only one or both to illustrate the importance and influence of factors. ...
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### How can the sum of two variables explain more variance than the individual variables?

I am getting some perplexing results for the correlation of a sum with a third variable when the two predictors are negatively correlated. What is causing these perplexing results? Example 1: ...
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### Is there a difference between semipartial correlation and regression coefficient in multiple regression?

I am preparing a presentation about multiple regression. Most of my sources seem to equal unstandardized coefficients in multiple regression with the semipartial correlation of that IV with the DV. ...
8k views

### Part correlation and R squared

This is the result I've got after running linear regression analysis in SPSS: I am a bit confused why the sum of squared part correlations is not equal to (or less than) R squared, but rather exceeds ...
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### How to tell if my variable is a suppressor?

I am analyzing data using path analysis and I am hoping someone here can help. In my model, I am looking at predictors of a variable, $Y$. In the path model, $Y$ has 4 significant predictors lets ...
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### Is it better to assess the strength of regression predictors using semipartial correlations or standardized coefficients?

I have been told in the past that semipartial coefficients are better, but I do not remember why that is meant to be the case. A google search seems to reveal that many researchers use one or the ...
344 views

### Why ever use F-statistic?

We can use F-statistic for determining whether at least one of the predictors has an effect on the response. But why just not take minimal p-value across all predictors? It doesn't require introducing ...