Inference with linear regression.

We concluded our discussion of regression by considering several kinds of inference: point estimation (i.e., estimation of the regression parameters), confidence intervals and significance tests for the slope of a regression line, and prediction.

Linear regression.

Generally speaking, regression concerns expressing a parameter of a response variable (usually its mean) as a function of one or more explanatory variables. In linear regression the function is a linear function, i.e. a line if we have a single explanatory variable. We discussed this model and also the idea of least squares which is often used to estimate the regression line from data.

Introduction to correlation & regression.

For this last week we will quicky cover the basic concepts of regression. Regression is a broad family of statistical methods concerning the relationship between a quantitative response variable and one or more qantitative explanatory variables. (Actually, regression can be extended to the case where there are categorical variables as well, but we won’t get to that in this course.) The topic of correlation is closely related to regression. Here’s a link to the correlation coefficient applet.

Here is a link to the final examination information handout.

Design & analysis.

There is an important relationship between design and (statistical) analysis. The way in which a study is designed can and should be considered in how its data are analyzed, and the way in which we know we can analyze data helps define good and bad designs. Perhaps nowhere in statistics is this more clear than in the context of the family of statistical methods known as the analysis of variance.

We discussed three basic designs: completely randomized, randomized block, and factorial designs. More complicated designs use elements from these designs.

Now, as for the ultimate Journey song to play during a statistics course…I considered several but this is a classic. Go Neal.

If you prefer rap, how about

or

Comparison between the F and t tests, follow-up analyses.

When there are only two groups/samples, both the t-test and the F-test from ANOVA can be used to test the difference between two population means. We discussed the relationship between these two tests.

The F-test from ANOVA only tests whether or not g population means are equal or not. Follow-up analyses are usually necessary to determine which differences are statistically significant. There are a variety of ways to do this, but we discussed the simplest approach known as Fisher’s method. Other methods attempt to control for the probability of making one or more errors in g(g-1)/2 tests.

Note: There are two corrections to the Quiz 7. On problem 1(b), you do not need to compute the p-value. Part b of problem 3 should read something like A within-groups sum of squares of exactly zero, but a between-groups sum of squares greater than zero.