In: Statistics and Probability
What are influential observations and outliers in regression and how to determine them? Use Excel Analysis ToolPak to solve the following problem.
The following data show the annual revenue ($ millions) and the
estimated team value
($ millions) for the 32 teams in the National Football League
(Forbes website, February
2009).
Team Revenue Value
Arizona Cardinals 203 914
Atlanta Falcons 203 872
Baltimore Ravens 226 1062
Buffalo Bills 206 885
Carolina Panthers 221 1040
Chicago Bears 226 1064
Cincinnati Bengals 205 941
Cleveland Browns 220 1035
Dallas Cowboys 269 1612
Denver Broncos 226 1061
Detroit Lions 204 917
Green Bay Packers 218 1023
Houston Texans 239 1125
Indianapolis Colts 203 1076
Jacksonville Jaguars 204 876
Kansas City Chiefs 214 1016
Miami Dolphins 232 1044
Minnesota Vikings 195 839
New England Patriots 282 1324
New Orleans Saints 213 937
New York Giants 214 1178
New York Jets 213 1170
Oakland Raiders 205 861
Philadelphia Eagles 237 1116
Pittsburgh Steelers 216 1015
San Diego Chargers 207 888
San Francisco 49ers 201 865
Seattle Seahawks 215 1010
St Louis Rams 206 929
Tampa Bay Buccaneers 224 1053
Tennessee Titans 216 994
Washington Redskins 327 1538
a. Develop a scatter diagram with Revenue on the
horizontal axis and Value on the vertical axis.
b. Develop the estimated regression equation that can
be used to predict team value given the value of annual
revenue.
c. Construct a residual plot of the standardized residuals against
the independent variable.
d. Do the assumptions about the error term and model form seem
reasonable in light of the residual plot?
Soln
a)
Steps for Scatterplot in Excel
b)
Steps for Regression in Excel
Regression Output
Regression Equation
Value = 5.83 Revenue – 252.08
c)
d)
From the plot in part c we can conclude that the assumptions of about error terms are not satisfied and they suffer from heteroskedasticity. (Absence of constant variance leads to heteroskedestacity)