Math 151 , Day 11, Wednesday, Feb. 25, 2004 After class

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Questions about Exam material
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HW Day 11 for Day 13
Read  Ch. 2 (Examining relationships), (review pp. 78-91.) 2.2 (correlation) 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.101, fig. 2.9, and know and  be able to use facts 1 thru 7, p. 100  Also to find r using SPSS.  Read ahead, Moore 2.3 pp.106-112.

Scatterplots: Hand in on Monday if possible: Relationships & Scatterplots: 2.1 SPSS Scatterplot Handout:  Use the handout and govsal_vs_pay.sav  data file to use SPSS and answer questions 1-5 (page 3). p.87, 2.6 (SPSS) gas mileage p.89, 2.7 (SPSS) metabolism Using the pre-made data set, graph the males and females simultaneously.   If you want to print just the females, change the male points' color to white, or Exclude them from the graph (handout p. 2).   Save your data file and output file for problem 2.22, later. p. 95, 2.14 (SPSS) (teachers' pay vs.no HS) (This problem looks forward to Sec. 2.3, sort of)  p. 95, 2.13 corn plant density. (SPSS) Import the data from the text file. Notice how the data is entered for SPSS--not as displayed here! but with the first column giving planting rates and the second giving yield.  Make a scatterplot.  You can find means for the separate groups as we did before (in Explore, rates to the Factor list).  Graph the means by hand on your plot, and connect.

Read, to discuss

Optional (more practice)

Postpone Correlation till after Monday's lecture:

Correlation  Hand in Probably Wednesday A. Go to Text website,  http://www.whfreeman.com/scc, (see below), and play with the  Correlation/Regression Applet.  Create a data set of around 10-15 points with r = -.65 (close to it).  Add the meanX&meanY lines, and make a sketch of your result on your paper to hand in. (Or you can print it out like this: Hit the Printscreen while holding down the Alt button.  This puts the image of the active window on the Clipboard.  Open Word, do Edit>Paste.  Then you can print the Word document.) Using SPSS to find correl. coeff.  (Back page of handout: Analyze>Correlate>Bivariate) Hand in the scatterplots, write the correlation values, other info on your printout. B. Use the file educ-v-mortality.sav    This is median education level and mortality rate for 60 American cities.  Make a scatterplot showing mortality on the y (vertical) axis  vs. education on the x axis.  with the two outliers (lower left) labeled with their cities.  Find r for the data with the outliers, then delete** the two outliers and find r again.  Write the two r's on your printed graph. p. 106, 2.28 (SPSS) speed, gas (real))   p. 103, 2.23 (SPSS) calories  **To delete a case, click on the gray case number.  The whole row should show black (selected), except for first column.  Then Delete key deletes it. (Edit has an undo) Save both data files, original and deletions, to your disk.

Read, to discuss. I will ask about these Wednesday. Moore p. 99 Use data of 2.17.You graphed this by hand for Sec. 2.1.  Guess what r is; look in the back of the book to see how close you got. p. 106 2.29 blunders C.  Many communities find a strong positive correlation between the amount of ice cream sold in a given month and the number of drownings that occur in that month.  Does this mean that ice cream causes drowning?  If not, can you think of an alternative explanation for the strong association? D. Explain why one would expect to find a positive correlation between the number of fire engines that respond to a fire and the amount of damage done in the fire.  Does this mean that the damage would be less extensive if only fewer fire engines were dispatched?  Explain.

Op- tion- al

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Get Handout on SPSS Scatterplots etc. (Moore Ch. 3)
govsal_vs_pay.sav  is the file used for most of the handout.
Relationships--Scatterplots (Day 10)
Start here Monday
Correlation: (Sec. 2.2)The correlation coefficient r is a numerical measure for how strongly linear (and in what direction) the relationship is.  Doesn't substitute  for a scatterplot.

1. Measures relationship--same whichever variable is on the x-axis
2. "Correlation" --only for 2 quantitative variables
3. "Unitless"--original measurment units are "standardized out"
4. Sign of correlation coefficient matches direction of relationship
5. Between -1 and +1.  0: no linear relationship, +1 or  -1: perfect straight line.
6. Does NOT give info about curved relationships.
7. NOT resistant to outliers--quite sensitive.

Correlation experiments:
Website,  http://www.whfreeman.com/scc,
   Click Netscape toolbars to minimize them, if needed.
    Choose "Statistical Applets",  Correlation/Regression.  Play with data points, observing the Correlation Coefficient.
       Check in the "Show Mean X & Mean Y lines" box.  See how much is in each quadrant. Compare with above.
--You won't have to calculate a correlation coefficient by hand. 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.