Friday, September 11, 2009

Chapter 3 Exploring Linear Relationships

No CiCi's on Sunday, September 20. Let's give the Accel Math II kids a chance.

The focus of this unit will be on standards I D 1-5 plus inference for regression (IV A 8 and IV B 7). These topics can be found in Chapters 3 and 15 of the text.

First up, we look at graphs of bivariate data. You must be able to graph (x,y) pairs on the Cartesian plane. We will be finding the Least Squares Regression Line (y-hat = a + bx) and interpreting multiple measures of fit. R is not the answer!!! You will be expected to calculate the LSRL using tables and formulas. There will be a couple of formulas that you should memorize, but now is a good time to get the green formula sheet out to see the formulas that you will be provided on all tests.

The most important formula so far is the formula for residuals: y - y-hat = the observed minus the expected [for each value of y].

Be prepared for a lab in class on Wednesday. Dress appropriately.


Friday 9/11/09: In our short period today we investigated the deviations and the residuals and just barely got to the formula that uses the squared deviations and the squared residuals:
First The deviations = the predicted differences + the residuals
Second 1 - (the sum of the squared residuals)/(the sum of the squared deviations) = r^2
Did you get that? R-squared equals the portion of the squared deviation that is not the squared error part. In other words, it is the part of the deviations that we could have predicted.
TO get these sums of the squared values we used the lists in the calculator like this:

L1: the x values
L2: the y values

Ran LinReg L1, L2, y1

L3: the predicted values of y FORUMULA= Y1(L1)
L4: the squared residuals FORMULA= (L2-L3)^2
L5: the squared deviations FORMULA= (L2-mean(L2))^2

Then use the LIST MATH 5.sum (L4) and (L5) to get the sums of the squared errors SSE and the sum of the squared deviations SST, respectively.

The R^2 formula is then 1 - (SSE/SST).

Take notes on all of Chapter 3 for Monday. Our test is Thursday.

The formulas we used in class on Monday were

b = r * Sy / Sx.

r = (sum of (Z of x * Z of y))/(n-1)

a = y-bar minus b * x-bar

HW is at least three and no more than 15 problems from the Chapter review for Chapter 3. We will cover the aspects of inference for linear regression on Tuesday.


s = the standard error about the line= an approximation of the average residual for that LSRL

SEb = the standard error of the slopes of the regression line. You would expect the slope to vary by about this much on average when you used different points from the population to come up with a LSRL.

beta = the slope of the real relationship between x and y, is approximated by b

alpha = the real y-intercept of the real relationship between x and y, approximated by a

Confidence interval for the slope : b +/- about 2 * SEb

T-statistic for testing Ho: beta = 0
b/SEb



STUDY for the test.

Test date 9/17/09.

Preview Chapter 4 for homework. See you on Monday.