The second major application of statistical theory concerns “linear regression” — a technique for modeling the relationship between a dependent (response) variable and one or more independent (explanatory) variables.

As with most statistics, there are two aspects to this topic. The first is a mathematical certianty, given certain requirements are met. The second is a probabilistic uncertainty, given the data are representative of the parameter of interest. We will play nice in this module by assuming the assumptions are met by the variables.

Should those assumptions not be met, as is usually the case, then transformations, adjustments, and alternative modeling schemes should be used. However, such issues are in the purview of MATH/STAT 222: Linear Models. If this section of the couse interests you, I strongly suggest you take Linear Models in the future. It is an exciting course where we thoroughly cover the results of linear regression, how to fix the results when the requirements are not met, and how to better model the dependent variable using its characteristics.

Objectives

By the end of this module, the student will

• understand the simple linear regression model
• calculate the ordinary least squares (OLS) regression line
• calculate estimates of — and confidence intervals for — the effect parameters
• estimate the dependent variable given a value of the independent variable (including a confidence interval)
• know the assumptions/requirements of OLS regression

Readings

All readings are from our official textbook.

• Sections 8.1 to 8.7
• Guided Thought Questions

Example Scripts

The following R script provide some additional practice in statistical computing. Consider these to be required activities.

• OLS Regression

Statistical Computing Activity

• SCA 5: Linear Regression

Assignment

• Assignment 5: School Enrollment