Linear Regression in R, Step-by-Step

Key Takeaways

I like Stat Quest. Do you like Stat Quest? I like Stat Quest. And I hope you like Stat Quest, too. Hello, and welcome to Stat Quest. Stat Quest is brought to you by the friendly folks in the genetics department at the University of North Carolina at Chapel Hill. Today, we're going to be talking about doing linear regression in R. This particular Stat Quest is intended to be a companion video for the Stat Quest on linear regression. For this tutorial, I'm going to assume that you already know how to get your data into R, and instead, I'm going to focus on how to get that data into a linear regression model and how to interpret the results. This is how I created the data for the Stat Quest on linear regression. I created a data frame with two columns, weight and size. If I just type mouse.data and then press return, R will print out the data frame in a nice column format. I then use the plot function to plot the data on an XY graph. This is where I set up the actual linear regression. I call the function LM, which stands for linear models, and I pass it a formula, and I pass it the mouse data. The way I specified the formula means that size are considered to be the Y values and weight are considered to be the X values. The linear models function then calculates the least squares estimates for the Y intercept and the slope. In R, the meat of doing a regression is in the summary function. This function generates all kinds of output, and I'm going to walk through it one step at a time. The first line just prints out the original call to the LM or linear models function. After that, you get a summary of the residuals. Those are the distance from the data to the fitted line. Ideally, they should be symmetrically distributed about the line. That means you want the min value and the max value to be approximately the same distance from zero. Likewise, you'd like the first quantile or 1Q and the third quantile or 3Q to be equidistant from zero. Also, it's nice to have the median close to zero as well. This next section tells us about the least squares estimates for the fitted line. This value is for the intercept and this value is for the slope. The standard error of the estimates and the T value are both provided to show you how the P values were calculated. These P values test whether the estimates for the intercept and the slope are equal to zero or not. If they're equal to zero, that means they don't have much use in the model. Lastly, these are the P values for the estimated parameters. Generally speaking, we are usually not interested in the intercept, so it doesn't matter what its P value is. However, we want a P value for weight to be less than .05. That is, we want it to be statistically significant. A significant P value for weight means that it will give us a reliable guess of mouse size. If you were unable to read the actual P value, but could, for some reason, see the star to its right, then these codes would give you a sense of what the P value was. The next line, the residual standard error, is the square root of the denominator in the equation for F. The next line tells us the multiple R squared and adjusted R squared values. Multiple R squared is just R squared as I describe it in the StatQuest on linear regression. It means that weight can explain 61% of the variation in size. This is good. Generally speaking, the adjusted R squared is the R squared scaled by the number of parameters in the model. The next line tells us if the R squared is significant or not. This is the value for F. These are the degrees of freedom. And here's our P value. Again, this says that weight gives us a reliable estimate for size. Lastly, we can add the regression line to the XY graph we started drawing earlier. Hooray! We've made it to the end of another exciting StatQuest. If you like this video and want to see more like it, please subscribe. And if you have ideas for future StatQuests, feel free to put them in the comments below.