Math 151 , Fall '07 , Day 14 Mon. Sept. 24 Hit reload..after class.

HW Day 14 (Re)Read Ch. 4  pp. 99-105 (correlation) Check 4.14 thru 4.20.  You do not have to be able to calculate r by hand.  You should be able to guess roughly at an r for a swarm of data; as p.102, eg. 4.6, and know and  be able to use facts 1-4, p. 101, and cautions 1-4 p. 103. 
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.)  Continuing regression, p. 126-137.
Hand in
Correlation (thinking):
p. 112, 4.36 and 4.37 Applet explorations
p. 112, 4.34 and 4.35 correlation meaning

4.26 date heights again  You graphed this by hand.  r = .5653. Now answer the questions.

p. 109 4.25 b  running records again.  It's a little complicated in SPSS to get the r's for the separate groups, so get them by looking at the answers in the back of the book.  Answer the question.

A.  If women always married men who were exactly  two years older than themselves, what would be the correlation between the ages of husband and wife? (Hint: make  a data table and the corresponding scatterplot for 4 or 5 couples with different x's, and look at it.)

Correlation (computing & thinking)
SPSS Scatterplot Handout:
Do problem 6, p. 3.  Keep this with the previous work.

p. 104, 4.11 (SPSS) gas, speed: association but 0 correlation.  Find the means and draw the mean lines on your graph (by hand) to help explain the 0 correlation.

p. 104, 4.10 (SPSS) bird colonies again.  To add a data pair in SPSS just type them in a new row at the bottom.  To delete, click on the case number, which highlights the whole row, hit delete.

(This problem looks forward to Ch. 5, sort of
 p. 110, 4.28 corn plant density. (SPSS)  Notice how the data is entered for SPSS--not as displayed here! but with the first column giving Plants per acre and the second giving Yield.  Make a scatterplot.  Use your calculator to find the mean yields, and write these on your paper.  (Or You can find means for the separate groups in SPSS : in Explore, Plants to the Factor list).  Graph the means by hand with a pencil on your printed plot, and connect the means dots.  You won't get a straight line.

Regression (Ch. 5):  Start these, on a separate page. WILL be part of HW assigned next (Day 15):
 C. Use the SPSS Scatterplot handout and graph  the regression line for govsal on avgpay (as shown, back page), also the lines for the 4 separate groups (either on one graph or on panels.) Print them out and keep them.  Start answering questions 6-11, on p. 3 of the 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:
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

p. 112, 4.33  Do a rough sketch for yourself.

Look at all the graphs you make, and guesstimate the correlation coefficient (before you read or calculate it.)









Regression: 
Use
http://www.whfreeman.com/bps4e
Correlation and Regression applet .
p. 148, 5.55





Optional 
Do now if you need the practice:
Straight line graphing practice:
A.  y = -10 + 3x, graph for 2<x<10.
B.  y = 500 - 20x, graph for 0<x<10.
 
  Correlation:  Use
http://www.whfreeman.com/bps4e
Correlation and Regression applet (see Day 13 for details) 
to make different scatterplot 
patterns, and observe their r's.

4.28, I said to draw the line by hand.
SPSS can plot the line
 connecting means
 on your graph:
 Get in Edit mode, do, Insert> Fit line Summary>Dot-Line.
The dots for the means are too much like the data dots. 
Do Format>Graph Elements>Line, and change them.


 

Exam 2 a week from Friday: Day 19 (Oct. 5.  Day before break.  Let me know Right Away if you need to take the exam early (Wed. or Th.)).  Starts with Ch. 3, Normal distribution, tables.  Thru Ch. 4, and what we cover of Ch.5 through next Monday.  Sample exam available Fri.    One sheet of notes: I will give you paper copies of the Normal table.

Relationships:  (BPS4e, Ch. 4) Day 13    Homework questions?
Who are those outliers in the  educ-v-mortality.sav  plot?
Timeplots:  are scatterplots, where the x axis shows time. (often a lurking variable: plot data against order of taking observations)
Handout on SPSS Scatterplots etc. pp.1-3, p.4  , showing subgroups, labeling individual points.
govsal_vs_pay.sav  is the file used for most of the handout. (In SPSS for Class BPS folder)

Correlation Day 13
 r:
strength of LINEAR relationship.  -1 (perfect negative relationship) to +1 (perfect positive relationship).  No units.  Sensitive to outliers.  Look at quadrants made from mean lines to guesstimate it.

Start here Wednesday
Regression line: Ch. 5, Predicts or estimates a y (vertical) value for a given x (horizontal) value: Straight line!
     "Regressing y ON x" .
(Graphing a straight line:  pick an x-value at one end of the useful range.  Plug in to the formula and calculate the corresponding y.  Graph the (x,y) pair.  Repeat with an x value at the other end of the range.  Connect the 2 dots with a line (see pretest).  Insurance:  Pick a third x and calculate the y.  This point must also lie on the line, if you did it right.)

Experimenting  http://www.whfreeman.com/bps4e,  Correlation and Regression Applet.
SPSS--back of handout.  Govsal on avgpay

Formula yhat = a + b x.    Govsal = a + b avgpay   Govsal = 28,569.69 + 2.71*avgpay
      To predict or estimate a y-value for a given x-value, plug the x value into the formula and calculate.
                To do it graphically, use the Up-and-Over method (Fig. 5.1, p.116):
                    Find the x, go straight up to the line, then go over to the y-axis; that y-value is the predicted y.

         Calculating:  Montana (17,895, 55,502)   Govsal = 28,569.69 + 2.71*avgpay
           Predicted Govsal = 28,569.69 + 2.71*17,895 = 28,569.69 + 48,495.45 = 77,065.14  (higher than actual)

 a is y-intercept. is slope:  If x increases one unit, yhat increases b units.   (b multiplies the x-variable.)
  If you know that yhat increases 12 units for every one that x increases, you know that the slope of the line b = 12. 
            Governor's salaries increase (on the average across the states)  $2.71 for every increase of  $1 of average pay.
     This is a summary  of the linear relationship, in the same way that the mean of a distribution is one summary of the distribution.  Particular states won't match this exactly.

 (In a straight-line relationship, the amount that y increases for one unit increase in x is the same no matter what value of x you start with)  RegressionSlope.xls or in ClassMaterial\Math151-BPS4e \RegressionDemos Excel BPS4e

We all get the same line from a batch of data because we use the "least-squares best fit" criterion (p. 119): we'll investigate this more closely later. At first, let SPSS or the text find the line for us; then we'll learn a way to calculate it from the data.

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