# Unit 1: Exploratory Methods and Inference in Case CQ

## Learning Objectives

Introduction to Regression

• Define regression analysis.
• Explain the reasons regression analysis can be used in practice.
• Recognize common statistical analyses which can be put into a regression framework.
• Define the steps in regression analysis.
• Define the types of regression models.
• Explain how linear regression with a continuous outcome models the average value of the response as the values of predictors change.
• Define the two essential ingredients in regression models.

Exploratory Data Analysis

• Discuss how exploratory data analysis is useful in the regression analysis process.
• Explain the process of data checking including useful methods and common types of errors.
• Determine types of variables.

Exploratory Data Analysis for One Variable

• Choose appropriate exploratory data analysis methods based upon the types of variables.
• Provide a written summary of the distribution of one variable based upon SAS output using appropriate methods.
• Correctly use and interpret Normal Quantile-Quantile plots .
• Create transformations of quantitative variables and conduct exploratory data analysis on the transformed variable.
• Perform exploratory data analysis for one variable in SAS.

Exploratory Data Analysis for Two Variables

• Choose appropriate exploratory data analysis methods based upon the types of variables.
• Provide a written summary of the observed association between two variables based upon SAS output using appropriate methods.
• Perform exploratory data analysis for two variables in SAS.

Exploratory Data Analysis for Multiple Variables

• Choose appropriate exploratory data analysis methods based upon the types of variables.
• Provide a written summary of any patterns when investigating multi-variable associations based upon SAS output using appropriate methods.
• Perform exploratory data analysis for multiple variables in SAS.

Review of Important Statistical Concepts

• Define parameters, statistics, sampling distributions, standard error, bias, variability of estimators, p-values, errors in hypothesis testing, and power
• Correctly use and interpret confidence intervals and hypothesis test results.
• Explain practical/clinical Significance vs. statistical significance.
• Explain association vs. causation

Review of Inference in Case CQ

• Use appropriate inferential methods in Case CQ where we have one categorical predictor and one (reasonably continuous) quantitative outcome.
• Perform appropriate data analysis in SAS.

Preview of Multi-Variable Inference

• Explain a data situation resulting in a two-way ANOVA model.
• Explain a data situation resulting in an ANCOVA model.
• Explain the concept of an interaction between two predictors.
• Determine the significance of an interaction term in a two-way ANOVA or ANCOVA model.
• Based upon interaction plots, discuss the effects of interest in context.