Instructions are found in the Linear Project module and examples. this project have different phases. The phase 1 is to post your Linear Model Topic and your Data (SEE EXAMPLE FROM STUDENT ATTACHED IN

First we graph the data points ( x, y) to get a scatterplot. Take the data, determine an appropriate scale on the horizontal axis and the vertical axis, and p lot the points, carefully labeling the scale and axes. Summer Olympics:

Men's 400 Meter Dash Winning Times Year (x) Time(y) (seconds) 1948 46.20 1952 45.90 1956 46.70 1960 44.90 1964 45.10 1968 43.80 1972 44.66 1976 44.26 1980 44.60 1984 44.27 1988 43.87 1992 43.50 1996 43.49 2000 43.84 2004 44.00 2008 43.75 Burger Fat (x) (grams) Calories (y) Wendy's Single 20 420 BK Whopper Jr. 24 420 McDonald's Big Mac 28 530 Wendy's Big Bacon Classic 30 580 Hardee's The Works 30 530 McDonald's Arch Deluxe 34 610 BK King Double Cheeseburger 39 640 Jack in the Box Jumbo Jack 40 650 BK Big King 43 660 BK King Whopper 46 730 Data from 1997 If the scatterplot shows a relatively linear trend, we try to fit a linear model, to find a line of best fit.

We could pick two arbitrary data points and find th e line through them, but that would not necessarily provide a good linear model representative of all t he data points.

A mathematical procedure that finds a line of "best fit" is called linear regression . This procedure is also called the method of least squares, as it minimizes the sum of the squares of the deviations of the po ints from the line. In MATH 107, we use software to find the regression line. (We can use Microsoft Excel, or Open Office, or a hand-held calculator or an online calculator --- more on this in the Technology Tips topic.) Linear regression software also typically reports p arameters denoted by r or r 2.

The real number r is called the correlation coefficient and provides a measure of the strength of the linear relationship. r is a real number between 1 and 1.

r = 1 indicates perfect positive correlation --- t he regression line has positive slope and all of th e data points are on the line.

r = 1 indicates perfect negative correlation --- the re gression line has negative slope and all of the data points are on the line The closer | r| is to 1, the stronger the linear correlation. If r = 0, there is no correlation at all. The following examples provide a sense of what an r value indicates. Source: The Basic Practice of Statistics , David S. Moore, page 108. Notice that a positive r value is associated with an increasing trend and a negative r value is associated with a decreasing trend. The strongest linear mode ls have r values close to 1 or close to 1.

The nonnegative real number r 2 is called the coefficient of determination and is the square of the correlation coefficient r. Since 0 | r| 1, multiplying through by | r|, we have 0 | r| 2 | r| and we know that 1 r 1.

So, 0 r 2 1. The closer r 2 is to 1, the stronger the indication of a linear relationship. Some software packages (such as Excel) report r 2, and so to get r, take the square root of r 2 and determine the sign of r by observing the trend (+ for increasing, for decreasing).