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R-squared

Measures of Model Fit for Linear Regression Models

by Karen Grace-Martin 37 Comments

A well-fitting regression model results in predicted values close to the observed data values. Stage 2

The mean model, which uses the mean for every predicted value, generally would be used if there were no useful predictor variables. The fit of a proposed regression model should therefore be better than the fit of the mean model. [Read more…] about Measures of Model Fit for Linear Regression Models

Tagged With: F test, Model Fit, R-squared, regression models, RMSE

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The Difference Between R-squared and Adjusted R-squared

by Karen Grace-Martin 2 Comments

One of the most useful and intuitive statistics we have in linear regression is the Coefficient of Determination: R²

It tells you how well the model predicts the outcome and has some nice properties. [Read more…] about The Difference Between R-squared and Adjusted R-squared

Tagged With: Adjusted R-squared, Coefficient of determination, linear regression, Multiple Regression, R-squared

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Simplifying a Categorical Predictor in Regression Models

by Jeff Meyer Leave a Comment

One of the many decisions you have to make when model building is which form each predictor variable should take. One specific version of this decision is whether to combine categories of a categorical predictor.

The greater the number of parameter estimates in a model the greater the number of observations that are needed to keep power constant. The parameter estimates in a linear [Read more…] about Simplifying a Categorical Predictor in Regression Models

Tagged With: categorical predictor, interpreting regression coefficients, Model Building, pairwise, R-squared

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Member Training: The Anatomy of an ANOVA Table

by Jeff Meyer

Our analysis of linear regression focuses on parameter estimates, z-scores, p-values and confidence levels. Rarely in regression do we see a discussion of the estimates and F statistics given in the ANOVA table above the coefficients and p-values.

And yet, they tell you a lot about your model and your data. Understanding the parts of the table and what they tell you is important for anyone running any regression or ANOVA model.

[Read more…] about Member Training: The Anatomy of an ANOVA Table

Tagged With: ANOVA, estimate, estimation, F test, R-squared, residuals, sum of squares, tables, types

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Two Types of Effect Size Statistic: Standardized and Unstandardized

by Karen Grace-Martin Leave a Comment

Effect size statistics are all the rage these days.

Journal editors are demanding them. Committees won’t pass dissertations without them.

But the reason to compute them is not just that someone wants them — they can truly help you understand your data analysis.

What Is an Effect Size Statistic?

When many of us hear “Effect Size Statistic,” we immediately think we need one of a few statistics: Eta-squared, Cohen’s d, R-squared.
And yes, these definitely qualify. But the concept of an effect size statistic is actually much broader. Here’s a description from a nice article on effect size statistics:

“… information about the magnitude and direction of the difference between two groups or the relationship between two variables.”

– Joseph A. Durlak, “How to Select, Calculate, and Interpret Effect Sizes”

If you think about it, many familiar statistics fit this description. Regression coefficients give information about the magnitude and direction of the relationship between two variables. So do correlation coefficients. [Read more…] about Two Types of Effect Size Statistic: Standardized and Unstandardized

Tagged With: Cohen's d, effect size statistics, Eta Squared, power calculation, R-squared, sample size estimates

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Can a Regression Model with a Small R-squared Be Useful?

by Karen Grace-Martin 57 Comments

R² is such a lovely statistic, isn’t it?  Unlike so many of the others, it makes sense–the percentage of variance in Y accounted for by a model.

I mean, you can actually understand that.  So can your grandmother.  And the clinical audience you’re writing the report for.

A big R² is always good and a small one is always bad, right?

Well, maybe. [Read more…] about Can a Regression Model with a Small R-squared Be Useful?

Tagged With: effect size, R-squared

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