Scatter Plots and Equations of Lines

First the Data Data must be collected and organized. For this example, you will be asked to write down some data about people you may know. Use your best estimate, even if you do not know that person. Decide quickly, and write it down.

How old are they, really?

Mick Jagger

Ashley Tisdale

Keanu Reeves

Angelina Jolie

Justin Timberlake

Cher

Jamie Foxx

Taylor Swift

Tony Hawk

Hillary Duff

Hugh Jackman

Drew Barrymore

George Clooney

Madonna

Tom Cruise

Jennifer Aniston

Johnny Depp

Julia Roberts

Jay Leno

Paula Abdul

Data . . . Now what? The ages you have estimated will serve as our input. We will now reveal the true age (in 2011) of the celebrities you have just seen. Write this actual age in the appropriate column on your data sheet. These will be our output.

Ready? Some of these may surprise you! Celebrity Date of Birth Age in 2011 Mick Jagger July 26, 1943 68 Ashley Tisdale July 2, 1985 26 Keanu Reeves September 2, 1964 47 Angelina Jolie June 4, 1975 36 Justin Timberlake January 31, 1981 30 Cher May 20, 1946 65 Jamie Foxx December 13, 1967 44 Taylor Swift December 13, 1989 22 Tony Hawk May 12, 1968 43 Hillary Duff September 28, 1987 24

Celebrity Date of Birth Age in 2011 And . . . Celebrity Date of Birth Age in 2011 Hugh Jackman October 12, 1968 43 Drew Barrymore February 22, 1975 36 George Clooney May 6, 1961 50 Madonna August 16, 1958 53 Tom Cruise July 3, 1962 49 Jennifer Aniston February 11, 1969 42 Johnny Depp June 9, 1963 48 Julia Roberts October 28, 1967 44 Jay Leno April 28, 1950 61 Paula Abdul June 19, 1962 49

The Scatter Plot Follow these steps to create a scatter plot on your graphing calculator: First Clear the RAM ( 2nd, + , 7 , 1 , 2 ) STAT, 1:Edit , then fill L1 with your estimates. Now, fill L2 with the actual ages.

The Scatter Plot continued: 2nd , STAT PLOT , 1:Plot 1 , Enter ( to turn on) ZOOM , 9:Zoom Stat There’s your scatter plot! Sketch it neatly in a calculator window in your notebook.

The Line of Best Fit Follow these steps to calculate the line of best fit on your graphing calculator: 2nd , 0 , “D” , scroll down until the arrow points to “Diagnostic On” , Enter , Enter. STAT , CALC , 4 , VARS , Y-VARS , 1:Function , 1:Y1 , Enter Write down your equation, rounding values to the nearest thousandth, if necessary. Graph!

How did you do? Do you tend to estimate too high, or too low? If you followed your equation to calculate your age, how old would you be?

Reflections: A scatter plot is a graph of data points which shows the relationship (correlation) between the two values being measured. A line of best fit is used as a best approximation of a summary of all the points in a scatter-plot. This line, or the equation of the graph of the line, can be used to make predictions about other possible outcomes.

Reflections: The correlation coefficient is a measure of how well the predicted values, or estimates, "fit" with the real- life data. The correlation coefficient (r2) is a number between 0 and 1. If there is no relationship between the predicted values and the actual values, the correlation coefficient is very low . A value of 0 would mean that the predicted values are no better than random numbers. A perfect fit gives a coefficient of 1.0 and means that the output is 100% predictable by the input using the equation of the line of regression.