**Overview**

In Module 7, we begin conducting bivariate analysis. Toward this end, the Module introduces various tools for examining linear relationships between variables and testing them for statistical significance. In particular, the Module moves from measures of joint fluctuation such as covariance and correlation to bivariate linear regression.

**Objectives**

- Calculate covariance and correlation as well as explain what these measures capture conceptually.
- Explain how the OLS regression line helps us model the relationship between two variables.
- Perform bivariate OLS regression in R and interpret the regression output.

**Assignment**

Assignment 3 is due at 11:59pm CST on Monday, 3/01. The Assignment 3 RMD file can be downloaded at the “Files/Exercises and Assignments” section at Canvas. Be sure to download and review the file early in the week so that you can plan your time accordingly.

**Module**

The video lectures for this week kick off with a *very* brief review of some of the assumptions that power the Central Limit Theorem. Watch the video on “CLT assumptions revisited” (I note that this title differs from the text shown on the title slide of my presentation.)

Let’s now turn to the central topic for this week’s Module: bivariate analysis. Note that so far, we have been performing what’s known as “univariate” analysis. This means that we have been examining *single* variables rather than relationships *between* variables. For instance, in Module 6, we focused primarily on the mean of a single variable such as annual income. (Recall our running Somersville example.) We then used hypothesis tests to assess whether some observed value of our sample mean provided evidence to refute some hypothesized value of the underlying population mean.

For the remainder of the quarter, we turn our attention to “bivariate” and “multivariate” analysis. That is, we will examine relationships *between* two or more variables. Ultimately, the basic procedures for such analysis are very similar to those we have used up until now: We will use sample statistics to estimate population parameters; we will calculate the typical error associated with our estimates; we will construct CIs; we will calculate test statistics; and we will perform hypothesis tests.

**Measures of join fluctuation**

Start by reading Imai, K. (2017). *Quantitative Social Science: An Introduction*. Read Sections 3.6, 4.2.1, and 4.2.2. The PDF is available at the “Files” section at Canvas.

Now watch the two videos on “Correlation” (*Introduction* and* Significance Tests*, respectively).

**Bivariate regression: Introduction**

Now read OIS Sections 7.1–7.4. Then, watch the video series on “Bivariate regression.” Note that I have divided what would normally be a single lecture into a series of short videos organized by sub-topic.

**Bivariate regression: The regression line**

**Bivariate regression: Calculating regression coefficients**

**Bivariate regression: Prediction, tests of significance, and interpretation**

Once you have completed your reading and watched the video lectures above, download and complete the Module 7 practice questions. They can be downloaded at the “Files/Practice Questions” section at Canvas.

Finally, be sure to download and complete Assignment 3, which is located at the “Files/Exercises and Assignments” section at Canvas.