How good of guesser ARE YOU????? The following contains pictures of famous (or not-so-famous) people. Without talking to anyone, write down your estimate of the age of each person (as of today) in the 2nd column. If you do not know the person, make a guess.

BARACK OBAMA

KENNY CHESNEY

MICHAEL JORDAN

JENNIFER LOPEZ

OPRAH WINFREY

KOBE BRYANT

TONY HAWK

BETTY WHITE

TIGER WOODS

LADY GAGA

DAVID BECKHAM

Dr. Phil

FLAVA FLAV

MRS. ASHBURN

MRS. CHILDREY!

In the first column, write down the person’s actual age. TIME FOR THE ANSWERS! In the first column, write down the person’s actual age.

BARACK OBAMA Born: August 4th, 1961 Age:57 years old

KENNY CHESNEY Born: March 26, 1968 Age: 50 years old

MICHAEL JORDAN Born Feb 17, 1963, Age 55 years old

JENNIFER LOPEZ Born: July 24th , 1969 Age: 49 years old

OPRAH WINFREY Born: January 29th , 1954 Age: 64 years old

KOBE BRYANT Born: August 23, 1978 Age: 40 years old

TONY HAWK Born: May 12th , 1968 Age: 50 years old

BETTY WHITE Born: January 17, 1922 Age: 96 years old

TIGER WOODS Born: December 30th, 1974 Age: 43 years old

LADY GAGA Born: March 28th, 1986 Age: 32 years old

DAVID BECKHAM Born: May 2nd, 1975 Age: 43 years old

Dr. Phil Born: September 1st, 1950 Age: 68 years old

FLAVA FLAV Born: March 16th, 1959 Age: 59 years old

MRS. ASHBURN Born: October 7th, 1985 Age: 32 years old Wish her a Happy Birthday before you leave on Friday!

Mrs. Childrey! Born: September 10,1970 Age: 29 years old—HAHA!

Is there a correlation??? After you have plotted all your points (there should be 15 total), describe the form, direction, strength, and unusual features of the scatter plot in question #1.

Find the best-fit line Put the points in your calculator under the STAT Edit.. Calculate the best fit line (make sure your diagnostic is on) CATALOG (2nd “0”  “DiagnosticOn”  ENTER) STAT CALC  option 8: LinReg a+bx VARS  YVARS  1: Function  1: Y1 ENTER Look at the graph (make sure your scatter plot is on) STAT PLOT  Plot 1  ON ZOOM  ZoomStat (#9) Write as an equation on your sheet (where it says “Algebraic (line of best fit)” (correlation coefficient will be in question #5)

Answer the questions On your paper, answer the rest of the questions.

How well does the LSRL fit the data? Now let’s calculate the residual values. Residuals show how far the points on the regression line are from the observed values. We calculate this by taking the observed value minus the predicted value. Residual = observed y – predicted y (or data – model )

Fill in the table Fill in the first column (actual age) and second column (your guessed age) of observed values In column 3, Calculate the LSRL prediction value for each person. For example, Obama is 57 years old, so substitute 57 in for x into your LSRL. In column 4, subtract column 2 – column 3

Residual Plot The Residual plot is a scatterplot of residuals against the explanatory variable. Residual plots help us assess how well a regression line fits the data.

Draw your residual plot Draw your residual plot on the given graph – remember the x-axis is the explanatory (or actual age) and the y-axis is the residual value.

Calc Tricks To plot the residuals: Stat, Edit, highlight L4, 2nd Stat (list), 7:Resid Stat Plot, 1st graph, X: L1, Y: L4 **Check your plot above in your calculator**

Two important things about residual plots: The residual plot should show NO obvious pattern. The graph should show a random scatter of points about the horizontal axis. The residuals should be relatively small in size. A regression line that fits the data well should come “close” to most of the points

Standard deviation of residuals (s) Whenever we use a least-squares regression line, the mean should be zero. That’s because the positive and negative residuals “balance out”. But that doesn’t tell us how far off the predictions are, on average. If we use a least-squares line to predict the values of a response variable y from an explanatory variable x, the standard deviation of the residuals (s) is given by: or This value gives the approximate size of a “typical” or “average” prediction error (residual)

Calculate your standard deviation! On your sheet, calculate the average prediction error of your LSRL   After seeing how your LSRL is “off”, do you feel comfortable making predictions with this regression line?

HOMEWORK Read Section 3.2—pp. 164-179 Do Sec 3.2 exercises #35, 38, 39, 40, 43, 47, 48, 53 Study for Quiz on 3.1