| Regression, Due Wed. Bring questions for exam, also. Problems in this color were given also
on W. Day 14, to work ahead. Repeated here. 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. Answer questions 6-9, 11, on p. 3 of the handout. Keep with the previous ones till you can answer all questions.(only 10, 12 to go) Hand in Wednesday-- 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. 118, 5.2 equation from info. As written, this is an algebra problem, not too hard, but not in the main focus of the course. I will tell you that the intercept is -50, and now the question is in the main focus of the course. That is, what is the slope, and what is the equation? p. 122, 5.4 (SPSS) Sparrowhawk colonies Use SPSS to make the scatterplot, with the line, and find r. Do (c) and (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. p. 139, 5.24 Penguins diving p. 148, 5.54 (Applet) regression suitability 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. A . Use the Excel RSquared page. ( R-Squared (or RSquared.xls: ClassMaterial\Math151BPS4e\RegressionDemosExcel BPS4e)If R-Squared doesn't have "repaired 10/3/06 in cell 2-o, use this link: R-Squared2 )). Shift points around and get an r2 close to .8 (80%) (Between .75 and .85 is good enough.). Note that if r = +.9, then r2 = .81. Now shift the points so that r is negative and r2 is close to .8. Print the resulting page to hand in. (Data and graph) Income depends on height?! Read the article at the link and answer this. If your browser doesn't get the link, it's at http://aurora.wells.edu/~srs/Math151-Sp07/tallpeoplewin.htm a)What is "$789", and what kind of analysis did they do? b)What does my footnote at the end tell you about the data that the article did not? B. With the SPSS Scatterplot handout, now do #10 also. (keep them all till we do #12) |
Read, to discuss 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) |
Op tion al
|
Mondays & WednesdaysAre you having trouble seeing which variable goes on the x axis? If there is any sense that one is the cause of the other, or can/will be used to predict or estimate the other, that's the explanatory (x) variable. The other one is the response (y) variable. (Sometimes you can choose the x-values and see the response for that x, in the corresponding y: like the corn plant density problem (It's an experiment, Ch.9.) Sometimes you can only observe.) Language: Regress heating oil ON temperature: Temperature = x = horizontal, Heating oil = y = vertical.
8:30 p.m. - 10:30 p.m.
Thursdays
3:00 p.m. - 7:00 p.m.
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)
(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.)
a is y-intercept.
b is slope:
If x increases one unit, yhat increases b
units.
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
Income depends on height?!
What is "$789", and what kind of analysis
did they do? (HW)
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.
Facts: 1, 2 lite, 3 first. Then 4. Then 2 &Formulas p. 120, from 2&3.
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