Tag Archives: r squared

Statistics: Regression

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Introduction to Linear Regression

Linear regression is a method for determining the best-fitting line through a set of data. In a lot of ways, it’s similar to a correlation since things like r and r squared are still used. The one difference is that the purpose of regression is prediction. The best-fitting line is calculated through the minimization of total squared error between the data points and the line.

The equation used for regression is Y = a +bx or some variation of that. If you remember from algebra class, this formula is like Y=mx+b. This is because they are both the linear equation. Although you may be asked to report r and r squared, the purpose of regression is to be able to find values for the slope (b) and the y-intercept (a) that creates a line that best fits through the data. Continue reading →

Statistics: Correlation

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Introduction to Correlation and Regression

So far we’ve been talking about analyses which involve variables which are split up into categorical or discrete variables (ex. treatment A, B, C) compared to a dependent variable which is continuous (ex. plant height). However, there is a way to look at two variables which have continuous data: correlation. A correlation will tell you the characteristics of a relationship such as direction (either positive or negative), form (we often work with linear relationships), and strength of the relationship. Strength and direction can be understood with the number which is given at the end of an analysis (r).

A positive correlation is one in which the increased value of one variable results in the increased value of another. For example, height and weight – as height increased, weight also tends to increase. A negative correlation is one in which the increased value of one variable results in the decrease of another. For example, as the temperature outside increases, hot chocolate sales will decrease. This is what is meant by the direction of a correlation. An r-value with a negative sign in front of it means a negative correlation and one without a negative sign means a positive correlation. Continue reading →