# 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.

**Broad Course Objectives:**

**CO-1:**Select appropriate methods for a scenario; determine if a linear or a nonlinear approach is appropriate**CO-2:**Use statistical software for performing regression analysis in the SAS language**CO-3:**Test and interpret linear models for continuous outcome data (normal linear model)**CO-4:**Test and interpret models for categorical outcome data (logistic and Poisson regression)**CO-5:**Draw appropriate conclusions for both randomized designed experiments and observational studies**CO-6:**Communicate clearly to subject matter experts the purposes and results of complex statistical analysis, both orally and in writing.