Math 151 , Day 12, Wednesday, Sept 26, 2001 Corrected version (Sunday night)

--Exam 1 Friday, in class, closed book.   Bring a simple calculator. I will give you copies of the Normal table.
Covers through 2.2.  You will need to read SPSS output, but not tell how to produce any. You will need to calculate "by hand" a standard deviation for four numbers. (As well as medians, quartiles, etc.)    You will NOT have to calculate a correlation coefficient by hand, but you may need to "guesstimate" one for a scatterplot picture.  Problems like HW + some true-false or multiple choice types.
Any questions?

Correlation:  See Day 11
--You won't have to calculate a correlation by hand, but I'll do one to reinforce what the formula does.  This formula is a bad one for hand computation (roundoff error); if you must do one by hand, find the computational formula in an old textbook.
--Eyeballing:  sketch xbar and ybar lines, see how much data is in + quadrants, how much in - quadrants.

 Graphing Straight lines? p. 124, 2.39, 2.40
Correlation with SPSS: we'll do these with the next section:
Section 2.3, Regression line:  Predicts or estimates a y value for a given x value.
    Formula yhat= a + b x.
         To predict a y-value for a given x-value, plug the x into the formula and calculate.
                To do it graphically, use the Up-and-Over method (Fig. 2.10, p.107):
                    Find the x, go straight up to the line, then go over to the y-axis; that y-value is the predicted y.
        a  is y-intercept. b  is slope:  If x increases one unit, yhat increases b units.

    Using SPSS to:
        DRAW line(s):  In Chart Editor,  (Chart/Options: Fit Line: Linear Regression)
        Calculate formula:  Statistics Analyze/Regression/Linear,
            Statistics button: Regression coefficients: check Estimates & Model Fit.
            Scroll output down to "Coefficients".  B column.  (Constant) = a, number under it = b.
                 yhat = a + bx
               Beta column.   This number is the correlation coefficient r.
              Regression coefficients       This is SPSS manual 2.1, p. 62. See Subgroups handout also.

 For Monday: Read  2.3 (Regression) through p. 114.
Day 12, Hand in on Monday, Day 14
A. Work through the SPSS manual, Section 2.1, pp.62-66.  Hand in a graph like Fig. 2.6, and the table like Table 2.3.  Write on the paper the correlation coeff. r, and the equation of the regression line.
B.  In Macmillan 101, open the Excel file RegressionSlope in the folder RegressionDemos in ClassMaterial\Math151.  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. 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.  Print the page to hand in.

p. 111, 2.31 acid rain No data, therefore no SPSS (draw the line by hand)
Be sure to write down the Regression line equation! Raw SPSS output isn't enough.
2.32 From SPSS,  Print the plain graph, and one with the regression line. Draw the regression line BY HAND as best you can on the plain graph. Check with the other one.  For b, pencil in the new points on the graph with the printed line. Find the mean by hand(calculator)...
p. 126, 2.44 & 48 Sarah grows.... Use SPSS for parts a and b, calculator for the rest.

Try the following, but keep to hand in with Day 14 (Monday's new work)  Monday I'll go over getting results from subgroups, and finding r in the SPSS output.
For the data of p103, 2.22 (metabolism), Print out a graph with the regression line for all the people, and another with 2 separate lines (M and F: Fit line:Subgroups). Use the "up and over" method of Fig. 2.10 p. 107, with a pencil and straightedge, to predict (graphically) the metabolic rate for
    a) a person of mass 45 kg.
    b) a female of mass 45 kg.
    c) a male of mass 45 kg.     (use a different line for each.  Write down your numerical answers, estimated from the graph scale.)

Using SPSS to find correl. coeff.  Hand in the scatterplots, write the correlation values, other info on your printout.
p. 106, 2.28 speed, gas (real) 

p. 103, 2.23 calories (manual,sec. 0.10 tells how to delete. Save both data files. 

 Read,
to discuss 		 Optional 
 
 

 


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