An important part of conducting sound science involves interpreting data correctly. Unfortunately, we don’t do that very well. For example, we are fooled by regression to the mean, we report findings when there are none, and we are overconfident about statistical power and significance. As scientists and lay persons, we want to be certain about research findings. But statistics only
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In the first and second posts of this series, we performed simple linear regression of a continuous outcome on a single continuous predictor, but we also learned it is possible to include binary or categorical predictors in such regression models. How is this be done? The hsb2.csv dataset we have been using also contains the variable female where male participants
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In the previous post, we performed simple linear regression of science scores on reading scores from 200 students using ordinary least squares (OLS) estimation. This was done using Python’s Statsmodels package. What does the OLS output show and how should it be interpreted? Here is the figure of the individual subject data and the line of best fit, as well
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Hypothesis testing vs. Estimation Hypothesis tests require that populations are Normally distributed in order for the tests to be reliable. When samples are drawn from Normally distributed populations, the distributions of F or t statistics can be calculated for any given sample size, and the F or t statistic for a specific experiment can be obtained from the distribution. This
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We introduced simple linear regression in a previous series and learned how to perform it in R (1, 2). What is the theory behind simple linear regression? How is it used to understand relationships between variables? What is another way to perform it in Python? The hsb2.csv dataset (available here) contains demographic and academic test scores data from 200 students.
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In statistics, we often want to fit a statistical model to be able to make broader generalizations. An important type of statistical model is linear regression, where we predict the linear relationship between an outcome variable and a predictor variable. In this post we will learn how to perform a simple linear regression in R. See our previous post for
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