Review.

Today gave a quick overview of the final examination and distributed a study sheet (downloadable from Blackboard).

Inference with regression.

Today we focused on statistical inference with regression. As in other scenarios, we can estimate parameters, make confidence intervals for parameters, and conduct tests concerning parameters. Another kind of prediction that is new however is prediction. A regression model can be used to predict the unknown value of a response variable. A confidence interval for this prediction is called a prediction interval.

Introduction to regression.

This week we’ll be doing a quick overview of regression. I talked the idea of a statistical relationship between variables, by expressing the mean of a response variable as a mathematical function of the value of an explanatory variable. Linear regression uses a line as this function. We started talking about how to estimate the parameters of the regression line using the data and the concept of least squares.

 

ANOVA with more than one factor: main effects, interactions, and block designs.

Today we considered that ANOVA can be generalized to consider relatively complicated designs with two or more factors. In a two-way design, we can make inferences concerning the main effects of each factor, as well as their interaction. This partitions the between-groups variability into three distinct sources. If a factor is made from a preexisting characteristic of the units, then it can be used as a a blocking variable in what is sometimes known as a block design. The intention of a blocking variable is to control for an important source of variability.

Multiple comparisons.

Today after reviewing the three assumptions underlying inferences from ANOVA, I introduced the technique of multiple comparisons — namely the so-called Fisher’s method. I also discussed the issue of the familywise error rate in the context of multiple comparisons.