MATH 251, P&S I, Fall 2007, Sept. 14, Day 10 Corrected hw problem hit reload

Day 10,   Read Regression,   2.3, first to p. 140, then the rest.
Memorize formula for r (p. 124) and for slope b (p. 137)
SPSS scatterplot Handout :  Correlation p. 4, Linear Regression,top. rest of p. 4.
 
Hand in: 
Regression 2.3 , on material thru about p. 140. HW p. 145ff.
p. 145 2.41 IQ/reading--NO SPSS, just graph a straight line.
2.43, 2.44  river, perch, NO SPSS rate, prediction, intercept
Governors' Salaries HW:  add #7, #8, #9, # 11, keep it.
2.49 icicles again.  (SPSS)
2.46 pipe defects ('SPSS)
Do, but keep your results for the next assignment:
2.42 a, b (c next time) basketball NO SPSS
2.47a, b (c next time) social distress (SPSS)
 Read, discuss 

Regression 2.3
p. 168, 2.77 (Applet)  Also, add meanx&meany lines after your experimenting.

 Optional 
 

Play with RegressionSlope (or in the folder RegressionDemosExcel in ClassMaterial\Math251). 


HW Questions? Day 9 Check with your neighbor first... 
Was there too much?  SPSS too hard to find?  Hand in Monday if you need to.
Quiz today, end of class:  Normal distribution and tables.  68-95-99.7% rule, and problems like those on the Normal Probability Practice Handout .  I will give you copies of Table A; if you have a calculator that does this type of problem, you must show all the work (x <-->z, numbers from the paper table needed) to demonstrate that you can do the problem by hand.
- - - - - - - - - - - - -
Revisit Correlation Day 9

Regression line: Section 2.3, Predicts or estimates a y (vertical) value for a given x (horizontal) value: Straight line!  
    Nematodes (2.18): Made a regression CURVE!  (Well, broken line...)
    "Regression" with no other description means "Least squares best fit line"--STRAIGHT line.
Experimenting  http://www.whfreeman.com/ips5e,  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   
   a is y-intercept. b  is slope (b multiplies x, the horizontal value):  If x increases one unit, yhat increases b units.
     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.

         To predict 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. 2.12, p.134):
                    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)

          RegressionSlope.xls or in  ClassMaterial\Math251 IPS5e\RegressionDemosExcel

We all get the same line from a batch of data because we use the "least-squares best fit" criterion (pp. 135-6): we'll investigate this more closely later.

**The Regression line is trying to predict the "average y" for a given x (with the added requirement that it is a straight line).
--For a particular (xo, yo) pair in the data, yo is the observed y.  The y-value you get by plugging xo into the regression line formula is the predicted y.  The error = observed y - predicted y.  (Positive if the observed y is above the line) IPSp.135.
--The line is chosen to minimize these vertical errors.  Practice fitting "least squares best fit" lines with applet    http://bcs.whfreeman.com/ips5e.

The Error for a given x value is also called the residual--the unexplained, unaccounted for part of the y-value.
   For Montana, the Error = 55,502 -77,065 = - 21,993.  Montana's governor's salary is almost $22K less than we would predict for that average pay.

--Unless the data lies perfectly on a straight line, the line for predicting weight from height -- "regressing weight on height" --(for example) will NOT be the same line as that for predicting height from weight--"regressing height on weight".  (In-class demonstration)(The picture on p.140 is about this. )


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