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The Coefficient of Determination and Linear Regression Assumptions

We’ve discussed how the linear regression model works. But how do you evaluate how good your model is. This is where the coefficient of determination comes in. In this post, we are going to discuss how to find the coefficient of determination and how to interpret it. What is the Coefficient of Determination? The

Ordinary Least Squares Regression

In this post, we are going to develop a mathematical understanding of linear regression using the most commonly applied method of ordinary least squares. We will use linear algebra and calculus to demonstrate why the least-squares method works. For a simple, intuitive introduction to regression that doesn’t require advanced math, check out the previous

Residuals and the Least Squares Regression Line

In this post, we will introduce linear regression analysis. The focus is on building intuition and the math is kept simple. If you want a more mathematical introduction to linear regression analysis, check out this post on ordinary least squares regression. Machine learning is about trying to find a model or a function that

Type 1 and Type 2 Error

When you are testing hypotheses, you might encounter type 1 and type 2 errors. Identifying them and dealing with them is essential for setting up statistical testing scenarios. They also play a huge role in machine learning. What is a Type 1 Error in Statistics? When you reject the null hypothesis although it is

Z Score Table for Confidence Intervals

Negative Z Table These are z-values to the left of the mean. Positive Z Table These are z-values to the right of the mean. Two-Sided Z-Score Table These are z_Value to the left and the right of the mean.

Student’s T-Distribution

In this post we introduce student’s t-distribution and learn how to construct t-confidence intervals. The t distribution is usually applied when you want to estimate the mean of normally distributed data but the sample size is small and you don’t know the population standard deviation. Like the Chi-Square distribution, it relies on degrees of

Chi-Square Distribution Table

Looking for an intuitive explanation of the Chi-Square distribution? Check out the blog post I wrote on the Chi-Square distribution and degrees of freedom. For a step-by-step explanation on Chi-Square testing, check out my post on the Chi-Square test for independence and goodness of fit. This post table is part of a blog post

Chi-Square Distribution and Degrees of Freedom

In this post, we introduce the Chi-Square distribution discuss the concept of degrees of freedom learn how to construct Chi-Square confidence intervals If you want to know how to perform chi-square testing for independence or goodness of fit, check out this post. For those interested, the last section discusses the relationship between the chi-square

Hypothesis Testing and P-Values

Hypothesis testing in statistics allows you to make informed decisions using data.In a hypothesis testing scenario, you have a null hypothesis that represents the status quo. Through the collection and analysis of data, you try to refute the null hypothesis in favor of an alternative hypothesis. If your tests are statistically significant, you can