In this video I introduce the single exam question that will be used to teach this entire chapter. There is very little variation possible with simple linear regression questions, so this question will do a great job of preparing you for any short answer questions from Chapter 16 that may appear on your exam.
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The questions in this chapter involve A LOT of calculations. I’ll teach you a system that will allow you to get through them quickly and correctly. It all starts with setting up a table of the data, and finding the sum of each column…
Sometimes the exam question will require that you use an alternative set of formulas – other than the more efficient ones I teach in the rest of my videos. I walk you through the calculations of those alternative formulas here, and discuss how they affect the solution.
The least squares regression line ( also known as the least squares regression equation, or simply the regression equation) is usually the first question worth marks on a simple linear regression question. We did most of our calculations when we found the sums in an earlier video, so determining the values (coefficients) of this equation will be quick and easy!
What good is an equation if you don’t know what it means? Here I explain what the intercept and slope of the equation line mean. I do this in the context of the example that we’ve been following throughout these videos, but I also give you a general version of the interpretations that will work for any simple linear regression questions.
Regression is all about making predictions. When you make a prediction, you can expect to make mistakes (errors). The Standard Error of the Estimate measures how big of an error we can typically expect. I go through the calculation and the interpretation and introduce the Sum of Squares Error (SSE) along the way.
So far, everything we know about the relationship between x and y is based on the sample – and not a direct observation of the population that we’re trying to comment on. How do we know that we can trust the sample to accurately represent the population. The t-test of the slope addresses this issue.
We are investigating whether or not x can help us to predict y. Maybe it does – but does that give us the whole picture? Perhaps OTHER factors also influence the value of y. The coefficient of determination tells us just how much the value of the dependent variable (y) can be determined by the independent variable that we’re studying (x).
There are three ways to use regression to make predictions of the dependent variable (y). Here I discuss all three: point estimates of y, prediction intervals of y, and confidence intervals of the AVERAGE y.
There are two very closely related measures of relationship in the regression chapters:
- The Coefficient of Correlation
- The Coefficient of Determination
I explain the similarities and the differences between the two here.
Test your understanding of multiple linear regression – each question is accompanied by a mini-video lecture showing you how I decided which solution was the correct one.