Assignment 12

 "A small error in the beginning is a great one at the end." -- (St. Thomas Aquinas) Decline of Mathematical Knowledge (300 - 500): With the rise of Christianity, thousands of Greek books were burned by Romans and Christians, who saw these magnificent creations as having their foundation in paganism. In 640 came the conquest of Egypt by the Moslems. Omar, the Arab conqueror, believed that Greek literature conflicted with the teaching of the Koran. More Greek works were destroyed. Why did Herkimer put a burning candle on top of a wheelbarrow full of bricks? Answer: He wanted to lighten the load. Things Herky would like to know: If Americans throw rice at weddings, why don't Orientals throw hamburgers? Since light travels faster than sound, is that why some people appear bright until you hear them speak? Reading: Review Section 2.5, as necessary. Exercise: Pages 104-105/22-27. Use your TI-83. Write these problems up neatly. Do not get sloppy in your presentations.

 Mathematical word analysis:DIAGRAM: From the Greek roots dia (to pass through or join) and gram (written or drawn). It literally means "that which is marked out."

OK, good people, you want to be able to produce a scatterplot with your TI-83, and, if appropriate, calculate the least-squares regression line.

If necessary, review the ITEMS FOR REFLECTION in Assignment #11, where the steps for doing the above are outlined.

This is MATH POWER at its best.

If your calculator does not show r2 and r when you choose LinReg(ax+b), then you are in DiagnosticOff mode. You want DiagnosticOn. To accomplish this, go to the CATALOG menu. (This is above the 0 button.) Scroll down the list until you get to DiagonosticOff and DiagnosticOn. Choose the On option. You will now see r2 and r when you choose LinReg(ax+b).

While this is not required, you might take the AP STATISTICS link off the Hideaway Home Page, click on the SECTION SUMMARIES option, then check the links (3.1, 3.2, 3.3) for Chapter 3 (Examining Relationships). This is what the Advanced Placement Statistics students need to know about correlation, prediction lines, etc. You should be able to read and understand what is in most of these summaries.

Problem: The following data were obtained for the amount of rainfall (in inches) and the yield of bushels of oats per acre for a selected sample.

 Rainfall (x) 2.5 3 5.7 8 9.3 9.7 10.2 Bushels (y) 38 42 41 45 46 44 48

Calculate the least-squares regression line and use it to predict the yield when there are 7 inches of rain.

Solution (with communication):

Putting the x values in list L1 and the y values in list L2 and producing a scatterplot (not shown here), the data appears to follow a reasonably linear trend. Calculation of the least-square regression line (steps outlined in Assignment #11) yields

LinReg
y = ax + b
a = .9230021298
b = 37.04667099
r2 = .7763733105
r = .8811204858

Doing some rounding of figures, the requested prediction line is y = 0.92x + 37.05 with r = 0.88. When x = 7, the predicted y value is y = (0.92)(7) + 37.05 = 43.49. In other words, with 7 inches of rainfall we would predict a yield of 43.49 bushels of oats.