Class 39: Topic 28: Least Squares Regression

Held: Monday, 5 May 2008

Summary: We consider how one computes regression lines that summarize the expected relationship between explanatory and response variables.

Notes:

• Some work returned today. More work to be returned on Wednesday. Grade summaries to be returned on Friday (after you fill out evaluation forms).
• There will be another exam-lette on Wednesday, on Topics 26-28. Your grade on Exam 3 is 2.5*(Sum of exam-lettes).

• Handouts: Applet: Least Squares Regression; R Notes for Topic 28.
• Due: 27-9, 27-12, 27-18.

Overview:

• Where we've been, where we're going.

A Few Notes on Grading

I'm returning a lot of work today (and more on Wednesday).

Group work will be returned to one member of the group (usually alphabetically first).

I will be happy to discuss any and all of your grades with you.

For exam-lettes:

• I checked over your own grades for in-class ones and made a few updates.
• I graded the take-home ones and added notes.
• A few of you neglected to sign academic honesty statements and need to talk to me.

For Lightning Presentations:

• Procrastination, although sometimes unavoidable, is rarely a good thing
• I punted a little bit: If I had no evidence to the contrary (e.g., my notes from class, the papers you turned in), I assumed you did things well.
• I then added the points (max 24), added 1, multiplied by 4, and rounded to nearest letter grade.

For Memos:

• I read through the memo, marking some strengths and weaknesses.
• I filled out the rubric based on that read-through.
• All "agree" is a B+. (That is, doing everything right is significantly better than adequate, but certainly not exceptional.)
• Two "strongly agrees" (with only agrees elsewhere) moved you up to an A-. Three or more moved you up to an A.
• Two "disagrees" (with only agrees elsewhere) moved you down to a B.
• Three "disagrees" moved you down to a B-.
• "Strongly agrees" and "disagrees" cancel out.

For Peer-Reviews

• Default grade (comments on most sections for class peers): A-
• Many fewer comments: Lower grade
• Really good and lots of comments: A

Where We've Been, Where We Are, and Where We're Going

• For the remainder of the semester, we are considering quantitative variables.

Recent Topics

• Topics 19 and 20: What one sample tells us about one population
  • Topic 19: Confidence intervals
  • Topic 20: Tests of significance (how likely a particular hypothesized mean is)
  • A.k.a. t-tests.
• Topic 22: What two samples of the same variable from two populations tell us about the relationship between those two populations.
  • A.k.a. two-sample t-tests.
• Topic 23: What samples of two similar variables from one population (or samples of the same variables from two linked populations) tell us about the expected relationship of those two variables.
  • A.k.a. paired t-tests.

Current Topics

• We are currently exploring what a sample can tell us about the relationship between two different variables. (That is, we use two different variables from each observational unit.)
• Topic 26 explored visual ways to explore those relationships.
• Topic 27 developed a numerical way to represent these relationships.

Remaining Topics

• We will conclude by thinking about ways in which knowing a bit about relationships between two quantitative variables can help us make some predictions.
• That is, if we know that there is good correlation between two variables, and we know the value of one of the two variables for an observational unit, what can we say about the value of the other variable?
• Topic 28 considers another way to describe the relationships between variables, and how to use that description to make predictions.
• Topic 29 looks a bit more about the accuracy of those predictions.