Unit 6: Linear Regression
In this unit, we will discuss situations in which the mean of a population, treated as a variable, depends on the value of another variable. One of the main reasons why we conduct such analyses is to understand how two variables are related to each other. The most common type of relationship is a linear relationship. For example, you may want to know what happens to one variable when you increase or decrease the other variable. You want to answer questions such as, "Does one variable increase as the other increases, or does the variable decrease?” For example, you may want to determine how the mean reaction time of rats depends on the amount of drug in bloodstream.
In this unit, you will also learn to measure the degree of a relationship between two or more variables. Both correlation and regression are measures for comparing variables. Correlation quantifies the strength of a relationship between two variables and is a measure of existing data. On the other hand, regression is the study of the strength of a linear relationship between an independent and dependent variable and can be used to predict the value of the dependent variable when the value of the independent variable is known.
Completing this unit should take you approximately 4 hours.
6.1: The Regression Model
6.1.1: Scatter Plot of Two Variables and Regression Line
6.1.2: Correlation Coefficient
6.1.3: Sums of Squares
6.2: Fitting the Model
6.2.1: Standard Errors of the Least Squares Estimates
6.2.2: Statistical Inference for the Slope and Correlation
6.2.3: Influential Observations
This optional subunit will teach you about "Analysis of Variance" (abbreviated ANOVA), which is used for hypothesis tests involving more than two averages. ANOVA is about examining the amount of variability in the y variable and trying to see where that variability is coming from. You will study the simplest form of ANOVA, called single factor or one-way ANOVA. Finally, you will briefly study the F distribution, used for ANOVA, and the test of two variances.
Unit 6 Assessment
- Receive a grade