# Lesson 1: Statistical Inference Foundations

### Overview of this Lesson

This lesson provides a brief refresher of the main statistical ideas that will be a useful foundation for the main focus of this course, regression analysis, covered in subsequent lessons. To simplify matters at this stage, we consider univariate data, that is, datasets consisting of measurements of just a single variable on a sample of observations. By contrast, regression analysis concerns multivariate data where there are two or more variables measured on a sample of observations. Nevertheless, the statistical ideas for univariate data carry over readily to this more complex situation, so it helps to start as simply as possible.

 Key Learning Goals for this Lesson: Review the main ways to identify and summarize data numerically and graphically. Review the process of statistical thinking, which involves drawing inferences about a population of interest by analyzing sample data. Use the normal probability distribution to make probability calculations for a population assuming known mean and standard deviation. Use the normal probability distribution to make probability calculations for a sample assuming known standard deviation. Use a t probability distribution to make probability calculations for a sample using the sample standard deviation. Calculate confidence intervals for a population mean. Conduct hypothesis tests for a population mean using the rejection region and p-value methods. Calculate prediction intervals for an individual observation.