Linked Questions

1answer
16 views

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 $\beta_2$ ...
4answers
31k views

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 ...
4answers
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 ...
4answers
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 ...
5answers
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 ...
2answers
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, ...
4answers
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. ...
4answers
2k views

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: ...
2answers
6k views

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. ...
1answer
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 ...
2answers
4k views

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 ...
1answer
2k views

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 ...
1answer
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 ...
3answers
3k views

Regression coefficients seem to have the wrong sign; can I force them to have a specific sign?

I'm working with some real world data and the regression models are yielding some counterintuitive results. Normally I trust the statistics but in reality some of these things can not be true. The ...
1answer
3k views

Why is my shared variance negative?

I have two questions regarding standard multiple regression: Why is my shared variance a negative number? Should I only include the positive semipartial correlations when calculating uniquely ...

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