Chapter 4 Nonlinear relationships

Read through the list of goals at the end of the chapter frequently.

In this chapter you will work with bivariate quantitative data and relationships between two categorical variables. For the quantitative part, you will learn to "straighten" x-y data, that is to use a transformation function to create a new relationship between f(x) and g(y) that is approximately linear. Find the least-squares relationship between the transformed data, then find the inverse of the original transformation function to transform the model into a curve which passes through your original x-y data. It's pretty cool to accomplish this and magnificently powerful math.

The second part, the categorical part, covers conditional and marginal probabilities. For instance, break the class into m/f and soph/jun/sen identifiers. Each person falls into exactly one of the gender groups and exactly one of the class year groups. Overall, what is the likelihood that a randomly-selected person is in a particular class? What is the probability that they are a particular gender? If they are a girl, then what is the probability that they are a senior? If they are a senior, what is the probability that they are a guy? Also, if guys do better than girls in 1st period and guys do better than girls in 5th period, how could the combination of the two classes indicate that girls are doing better than boys?

Dress appropriately for the weather and for doing activities that involve sitting on the floor this week. See you 10/8 at CiCi's???

Chapter 3 Linear relationships

Now you've done it all! Can you

identify bivariate data?

graph response and explanatory variables?

differentiate in a scatterplot for a categorical variable?

describe data represented in a scatterplot?

find the least-squares regression line?

compare and contrast the concepts of regression, correlation, association?

explain what the correlation coefficient tells us?

explain what the coefficient of determination tells us?

use a predictor line (LSRL) to predict the value of y for a given x?

use a predictor line to calculate and interpret residuals?

calculate EVERYTHING using the formulas in the text?

explain the vocabulary?

identify the key topics from this chapter?

write good questions for a test?

teach someone else how to work these problems?

squeeze the maximum information from real data using linear methods appropriately?

prove (in writing) that you understand and can apply the concepts of this chapter?



What have I left out?

CU @ CiCi's.

Chapter 2 thoughts

Essential question: Why is the Normal distribution so special?


Here's a teaser for you--if you know that 20% of the data in a normally-distributed population fall below the x-value 306 and 80% fall below the value 772, can you find the mean and standard deviation of the population???

I will be in the classroom as early as possible on Thursday, but I have a parent meeting at 7:45. Please use your other resources well. Don't forget the book! The chapter summaries are great tools. Do the practice quiz online. Dream up questions that I might ask.

Have a slice of pizza for me.

Pre-test discussion

Ask and answer the most pressing questions here. You WILL nned to establish an identity to post. Please DO NOT use your first and last names.

Have you taken the practice quiz yet? The link is on the right edge of the main screen. Spread the word to your friends and neighbors.

Good luck.

Straightening data

Here's the plan we developed in class:

Load your (x,y) data into L1 and L2.
Look at them.

If they are not already straight, figure out if the ideal model would pass through the x-axis, the y-axis, or both. To save some time, try this to straighten your data:

Case 1: if the ideal model would cross the y-axis, take the ln of the observed y values. Case 2: if the model would cross the x-axis, take the ln of the x values, too.

THEN
Case 1: Run the linear regression on the original x and the ln y. Change your stat plot to show the (x, ln y) points with the linear regression equation. If this is a good fit, then the residuals will be scattered. Correct the linear regression equation to reflect that the y-values were really ln y. Solve the fixed equation for y.

Case 2: Run the linear regression on the ln x and the ln y. Change your stat plot to show the (ln x, ln y) points with the linear regression equation. If this is a good fit, then the residuals will be scattered. Correct the linear regression equation to reflect that the y-values were really ln y and the x-values were really ln x. Solve the corrected equation for y.

To check your results, put the new equation for y into the y= register to graph. Change your statplot to show the original data (x,y), probably in L1 and L2. The curve you generated should pass neatly through the data.

Note that this method finds the line which miniomizes the sum of the squared residuals from the STRAIGHTENED data, not the squares of the residuals from the curved fit.




Oh yeah, go Braves!

Welcome to the new school year

How is a permutation different from a combination? How are they similar?

Scores from the exam and a Must-see-video

I'd love to hear how you did on all of your AP exams and how your summer is going, but PLEASE do not use first and last names on the BLOG. YOu can send private emails to my school email if you want.

You guys are great!

I hope that you are done with your summer assignments so you can enjoy the last month! :)

You HAVE TO check out this video:
http://video.google.com/videoplay?docid=5243677894327730537


Let me know how you like it.

Mrs. L