Math 151 , Fall. '08, Day 14 Mon. Sept. 29 Hit reload.. .After class.

HW Day 14 For next:Ch. 5, Regression, thru p. 125 (check p. 137: 5.14 through 20, basic line and regression line facts and tools. 21 r and slope, 22 is harder--changing units--don't worry about it. 23 If you sketch the graph and draw a line thru the points, you should be able to guesstimate the slope well enough to choose among the 3 answers.)  ahead: Continuing regression, p. 126-137.

(Don't)Hand in next class:  (also hand in Day 13 if you haven't) Nothing new to hand in: You can/should start looking at these problems, but they'll all be assigned Wed. (Day 15)
Regression (Ch. 5): 
B. Use the SPSS Scatterplot handout and graph  the regression line for govsal on avgpay (as shown, p. 2), also the lines for the 4 separate groups (either on one graph or on panels.) Print them out and keep them.  Find the formula for the regression line (p. 4 of handout).   Answer questions 7-9, 11, on Governors' Salaries handout.  Keep the handout answers till you can answer all 12 questions.

p. 118, 5.1  IQ and reading scores. Graph, slope, predict.  Notice we don't have a scatterplot of the data, only this straight-line summary.
p. 139, 5.24 Penguins diving  Again, we don't have a scatterplot, only the summary.

p. 122, 5.4 (SPSS) Sparrowhawk colonies  Use SPSS to make the scatterplot, with the line, and find r.  Do (c),  and compute (d) by hand.    Now use the "up and over" method of Fig. 5.1, p.116, with a pencil and straightedge to mark the predicted value from (d) on the y-scale. Write down your computed answer next to it.  Make sure the two  methods give consistent answers.

Some more with SPSS--as long as you're at the computer, get r's, the graphs and lines, line formulas:  keep for next assignment
 p. 140, 5.26 (SPSS) sisters & brothers
p. 146, 5.42 (SPSS) A computer circle game  The last part of the last question, "Give numerical measures that describe the success of the two regressions,"  is asking for you to use Fact 4.

 Read to discuss
Go over your exam, with the Solutions; figure out what went wrong, & why.
Regression:
Use
http://www.whfreeman.com/bps4e, 
Correlation and Regression applet  to do p. 148, 5.55 , guessing lines

 Look at this especially, with reference to the r standard deviations in y for every 1 standard deviation in x: A. Open the Excel file RegressionSlope (or in the folder RegressionDemosExcelBPS4e  in ClassMaterial\Math151-BPS4e).  Change x-y values in the yellow boxes and watch the line change.  Change x-values in col. F and watch the "run" (red line) change, in the rightmost 2 graphs. Notice the slope = the coefficient of x = the rise/run = increase in y per unit increase in x.  Fix it so the increase in x (the "run") is exactly 1.   Also, look at the leftmost graph, where the length of the standard deviations are shown, and note that in standard-deviation units, the rise is r s.d.'s in y for each s.d. run in x.  (Fact 2)
 Optional 

Exams returned today.  Solutions
  Comments on selected problems.
We see that (at least for these 500 insured drivers) males tend to have more accidents.
 Are males worse drivers?  Alternative explanation(s)?
Think of lurking variables--such that males are NOT worse drivers, though they tend to have more accidents.

SPSS weekend unavailability--> Day 13 may be handed in Wed.  (Or, ideally, put it in the folder, or in the box, outside my door when finished.)
Correlation HW questions?  Day 13
P110, 4.28, corn plant density.  Made a regression CURVE!  (Well, broken line...)
   Note, can use line to predict a "typical" or average yield for a particular planting rate. 

New:= = = =Didn't get far: Continue on Wed. = = =
Regression line: Ch. 5, Predicts or estimates a y (vertical) value for a given x (horizontal) value: Straight line!  Details Day 13
Experimenting  http://www.whfreeman.com/bps4e,  Correlation and Regression Applet.
SPSS--graph line, p. 2 top of handout link.
     formula p. 4 of handout link. . Read off "coefficients" (intercept and slope) from table.
      Govsal on avgpay
Formula yhat = a + b x.  (yhat means we're finding a sort of average y for each particular x).
  Govsal = a + b avgpay  
a is y-intercept. b  is slope:  If x increases one unit, yhat increases b units.   (b multiplies the x-variable.)

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