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Statistics By Jim

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Regression

How to Interpret P-values and Coefficients in Regression Analysis

By Jim Frost 260 Comments


P values and coefficients in regression analysis work together to tell you which relationships in your model are statistically significant and the nature of those relationships. The linear regression coefficients describe the mathematical relationship between each independent variable and the dependent variable. The p values for the coefficients indicate whether these relationships are statistically significant. [Read more…] about How to Interpret P-values and Coefficients in Regression Analysis

Filed Under: Regression Tagged With: analysis example, conceptual, interpreting results

R-squared Is Not Valid for Nonlinear Regression

By Jim Frost 17 Comments

Nonlinear regression is an extremely flexible analysis that can fit most any curve that is present in your data. R-squared seems like a very intuitive way to assess the goodness-of-fit for a regression model. Unfortunately, the two just don’t go together. R-squared is invalid for nonlinear regression. [Read more…] about R-squared Is Not Valid for Nonlinear Regression

Filed Under: Regression Tagged With: assumptions, conceptual

How to Interpret Adjusted R-Squared and Predicted R-Squared in Regression Analysis

By Jim Frost 134 Comments

R-squared is a goodness-of-fit measure that tends to reward you for including too many independent variables in a regression model, and it doesn’t provide any incentive to stop adding more. Adjusted R-squared and predicted R-squared use different approaches to help you fight that impulse to add too many. The protection that adjusted R-squared and predicted R-squared provide is critical because too many terms in a model can produce results that you can’t trust. These statistics help you include the correct number of independent variables in your regression model. [Read more…] about How to Interpret Adjusted R-Squared and Predicted R-Squared in Regression Analysis

Filed Under: Regression Tagged With: analysis example, conceptual, interpreting results

How to Interpret the Constant (Y Intercept) in Regression Analysis

By Jim Frost 95 Comments


The constant term in regression analysis is the value at which the regression line crosses the y-axis. The constant is also known as the y-intercept. That sounds simple enough, right? Mathematically, the regression constant really is that simple. However, the difficulties begin when you try to interpret the meaning of the y-intercept in your regression output. [Read more…] about How to Interpret the Constant (Y Intercept) in Regression Analysis

Filed Under: Regression Tagged With: conceptual, graphs, interpreting results

Check Your Residual Plots to Ensure Trustworthy Regression Results!

By Jim Frost 65 Comments

Use residual plots to check the assumptions of an OLS linear regression model. If you violate the assumptions, you risk producing results that you can’t trust. Residual plots display the residual values on the y-axis and fitted values, or another variable, on the x-axis. After you fit a regression model, it is crucial to check the residual plots. If your plots display unwanted patterns, you can’t trust the regression coefficients and other numeric results.

In this post, I explain the conceptual reasons why residual plots help ensure that your regression model is valid. I’ll also show you what to look for and how to fix the problems. [Read more…] about Check Your Residual Plots to Ensure Trustworthy Regression Results!

Filed Under: Regression Tagged With: assumptions, conceptual, graphs

How to Interpret the F-test of Overall Significance in Regression Analysis

By Jim Frost 135 Comments


The F-test of overall significance indicates whether your linear regression model provides a better fit to the data than a model that contains no independent variables. In this post, I look at how the F-test of overall significance fits in with other regression statistics, such as R-squared. R-squared tells you how well your model fits the data, and the F-test is related to it. [Read more…] about How to Interpret the F-test of Overall Significance in Regression Analysis

Filed Under: Regression Tagged With: conceptual, interpreting results

Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

By Jim Frost 202 Comments


Multicollinearity occurs when independent variables in a regression model are correlated. This correlation is a problem because independent variables should be independent. If the degree of correlation between variables is high enough, it can cause problems when you fit the model and interpret the results. [Read more…] about Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

Filed Under: Regression Tagged With: analysis example, conceptual, interpreting results

The Difference between Linear and Nonlinear Regression Models

By Jim Frost 63 Comments

The difference between linear and nonlinear regression models isn’t as straightforward as it sounds. You’d think that linear equations produce straight lines and nonlinear equations model curvature. Unfortunately, that’s not correct. Both types of models can fit curves to your data—so that’s not the defining characteristic. In this post, I’ll teach you how to identify linear and nonlinear regression models. [Read more…] about The Difference between Linear and Nonlinear Regression Models

Filed Under: Regression Tagged With: conceptual

Standard Error of the Regression vs. R-squared

By Jim Frost 130 Comments


The standard error of the regression (S) and R-squared are two key goodness-of-fit measures for regression analysis. While R-squared is the most well-known amongst the goodness-of-fit statistics, I think it is a bit over-hyped. The standard error of the regression is also known as residual standard error.
[Read more…] about Standard Error of the Regression vs. R-squared

Filed Under: Regression Tagged With: analysis example, interpreting results

Statistical Analysis of the Republican Establishment Split

By Jim Frost 2 Comments

Back in 2014, House Speaker John Boehner resigned, and then Kevin McCarthy refused the position of Speaker of the House before the vote. The Republican’s search for a new speaker ultimately led to Paul Ryan. Simultaneously, the Republican Freedom Caucus was making the news with a potential shutdown of the government that was controversial even amongst some Republicans. [Read more…] about Statistical Analysis of the Republican Establishment Split

Filed Under: Regression Tagged With: analysis example, interpreting results

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    Top Posts

    • How to Interpret P-values and Coefficients in Regression Analysis
    • F-table
    • How To Interpret R-squared in Regression Analysis
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    • How to Find the P value: Process and Calculations
    • Weighted Average: Formula & Calculation Examples
    • T-Distribution Table of Critical Values
    • Cronbach’s Alpha: Definition, Calculations & Example
    • Multicollinearity in Regression Analysis: Problems, Detection, and Solutions

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