Work AT LEAST 5 problems to prepare for Thursday's test.
Monday, October 1
3.50 and 3.52
Test on Thursday
Friday,September 28
Yo, this is David T.
Well today we broke up the deviation in a prediction, part into y-hat minus y-bar and an error part y -y-hat.
We also explained the significance of r^2 which equals the portion of the variation in y which could have been predicted using the regression relation.
Remember that if r^2 is close to zero, then the points on the graph are crazy and scattered. If r^2 is close to one, then the graph and points are predictable and are linear.
The HW is 3.46 and 3.49. (YES, this means YOU!) You = David V.
Thursday, September 27
KEY FORMULAS
b = r * Sy/Sx
a = y-bar minus b* x-bar
y-hat = a + b* x
residual = actual minus expected = y - y-hat
If residuals are small and scattered, then the linear model is a good model. If there is a distinct pattern (if you could predict what the residual would be for a particular x-value), then the linear model is not appropriate.
Be sure to WRITE what you see in the residuals ("The residuals are small and scattered, so a linear model is appropriate" or not) and what effect that observation has on your model.
Also be sure to write out the description of the y-hat equation in words: "The predicted value of [insert y variable here] is approximately [insert y-intercept here] plus [insert slope here] times [insert the x variable here]."
COMMON ERRORS:
Failure to use LinReg(a+bx) L1, L2, Y1
Failure to check that the observed y values are close to the predicted y values.
Failure to use the same x and y in your stat plot that you used in your linreg equation. (causes graphs to not show up!)
HW problem 3.39.
Wednesday, September 26
Problems 23 and 31 PLUS find the Least squares regression line for the Archaeopteryx data.
Tuesday, September 25
We re-worked the HW from last night and extended the concept by investigating what happens when you calculate the correlation coefficient for non-linear data (Anarchy! Riots! Dogs and cats living together!). Although you CAN calculate a correlation coefficient for non-linear data, the results tells you NOTHING.
Key points to remember:
- -1<= r <= 1. Always. No getting around it.
- r is dimensionless. If you change units or perform a linear operation on all of the values of x, or y, or both, your r will not change!!! In fact, what happens when you switch the order of the variables and calculate r for L2 and L1????
- r is affected by outliers. They increase the standard deviation, which causes the denominator to be smaller, which causes the r to be closer to 0.
- r only gives you information about linear relationships. If it isn't linear, then this linear modeling is inappropriate.
HW 3.13 and 3.19. All about the archaeopteryx.
See you tomorrow.
Monday, September 24
Do problem 3.18. This is just like what we did in class.
Friday, September 21
Problems 3.1-3.3 and 3.5.
Fifth and sixth periods: You did a great job with all the distractions today. Thanks for trying to stay on task.
Good job, Trojans! You make us proud.
CiCi's on Sunday? 2-4.
Be safe.
A new Chapter!!!
Thursday, September 20
Copy the formulas and definitions from Chapter 3 into your notes.
Posts
9 comments:
Ms. Linner, I forgot how to work the correlation r formula w/out the calculator. You showed it to us on the board a few times, but I never wrote it down (woops), I'm stuck on when you have to put your x's over the Sx's and the y's over the Sy's and then you combine them or something like that. (?)
Ross, I hope that Wednesday's lesson helped resolve this.
Both x-bar and y-bar in our example were equal to zero, so when we standardized the values of x we got
(x minus x-bar)/sx.
Because x-bar was equal to x, this simplifies to x/sx. Likewise, the standardized y value became y/sy.
This is not going to happen in real life. You can probably expect the sample average of x and the sample average of y to be something other than zero.
I can't seem to find this in my book, but what's coeffiecient of determination and what does it mean? Is it r^2?
Ms. Linner, I'm having trouble understanding r^2 and other things that have to do with it, can I come in tomorrow morning at like 7:45 or something for some pointers? (and yes, this is my other username)
The coefficient of determination is introduced on page 147 of the text.
It IS r^2. It is the fraction of the variation in y that we could have predicted using the linear regression model.
If r^2 is .64, then 64% of the variation in y could have bee predicted. The rest of the variation is randomness.
I will be glad to see you in the morning.
Are there any other links or sites that would provide a quiz besides the one posted?
I googled linear regression quiz and found the following quiz:
http://www.asqsandiego.org/articles/Correlation_Regress-Quiz1.pdf
The answers are at the end. The multiple regression and autocorrelation parts are not part of our content, so (obviously) they will not be part of your test.
If you find a good quiz site, post a link!
I'm gonna dominate the test tomorrow Mrs. L. It's not going to know what hit it.
I hope that's true!
Sounds Like Mr. F is ready to field your questions, crew! Post your best guesses at what is on tomorrow's test and we'll see if anyone can answer the toughies.
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