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state sat takers income years public expend rank Iowa 1088 3 326 16.79 87.8 25.60 89.7 SouthDakota 1075 2 264 16.07 86.2 19.95 90.6 NorthDakota 1068 3 317 16.57 88.3 20.62 89.8 Kansas 1045 5 338 16.30 83.9 27.14 86.3 Nebraska 1045 5 293 17.25 83.6 21.05 88.5 Montana 1033 8 263 15.91 93.7 29.48 86.4 Minnesota 1028 7 343 17.41 78.3 24.84 83.4 Utah 1022 4 333 16.57 75.2 17.42 85.9 Wyoming 1017 5 328 16.01 97.0 25.96 87.5 Wisconsin 1011 10 304 16.85 77.3 27.69 84.2 Oklahoma 1001 5 358 15.95 74.2 20.07 85.6 Arkansas 999 4 295 15.49 86.4 15.71 89.2 Tennessee 999 9 330 15.72 61.2 14.58 83.4 NewMexico 997 8 316 15.92 79.5 22.19 83.7 Idaho 995 7 285 16.18 92.1 17.80 85.9 Mississippi 988 3 315 16.76 67.9 15.36 90.1 Kentucky 985 6 330 16.61 71.4 15.69 86.4 Colorado 983 16 333 16.83 88.3 26.56 81.8 Washington 982 19 309 16.23 87.5 26.53 83.2 Arizona 981 11 314 15.98 80.9 19.14 84.3 Illinois 977 14 347 15.80 74.6 24.41 78.7 Louisiana 975 5 394 16.85 44.8 19.72 82.9 Missouri 975 10 322 16.42 67.7 20.79 80.6 Michigan 973 10 335 16.50 80.7 24.61 81.8 WestVirginia 968 7 292 17.08 90.6 18.16 86.2 Alabama 964 6 313 16.37 69.6 13.84 83.9 Ohio 958 16 306 16.52 71.5 21.43 79.5 NewHampshire 925 56 248 16.35 78.1 20.33 73.6 Alaska 923 31 401 15.32 96.5 50.10 79.6 Nevada 917 18 288 14.73 89.1 21.79 81.1 Oregon 908 40 261 14.48 92.1 30.49 79.3 Vermont 904 54 225 16.50 84.2 20.17 75.8 California 899 36 293 15.52 83.0 25.94 77.5 Delaware 897 42 277 16.95 67.9 27.81 71.4 Connecticut 896 69 287 16.75 76.8 26.97 69.8 NewYork 896 59 236 16.86 80.4 33.58 70.5 Maine 890 46 208 16.05 85.7 20.55 74.6 Florida 889 39 255 15.91 80.5 22.62 74.6 Maryland 889 50 312 16.90 80.4 25.41 71.5 Virginia 888 52 295 16.08 88.8 22.23 72.4 Massachusetts 888 65 246 16.79 80.7 31.74 69.9 Pennsylvania 885 50 241 17.27 78.6 27.98 73.4 RhodeIsland 877 59 228 16.67 79.7 25.59 71.4 NewJersey 869 64 269 16.37 80.6 27.91 69.8 Texas 868 32 303 14.95 91.7 19.55 76.4 Indiana 860 48 258 14.39 90.2 17.93 74.1 Hawaii 857 47 277 16.40 67.6 21.21 69.9 NorthCarolina 827 47 224 15.31 92.8 19.92 75.3 Georgia 823 51 250 15.55 86.5 16.52 74.0 SouthCarolina 790 48 214 15.42 88.1 15.60 74.0

2. The data set is from the first year that SAT scores were published on a state-by-state basis in the U.S. It was originally published in the Harvard Educational Review in 1984, and is also reported in Ramsey and Schafer, 1997. The variables included are:

sat =averagetotalSATscoreforthestate takers =percentofeligiblestudentsinthestatewhotooktheexam income =themedianfamilyincomeofstudentsinthestatewhotooktheexam years =theaveragenumberofyearsthatthetest-takers had for studies in the core subjects public =percentageoftesttakersattendingpublicsecondaryschools expend =thestatesexpendituresoneducationinhundredsofdollarsperstudent rank =themedianpercentilerankingofthetest-takers in their high-school class

Perform a multiple regression to predict the average SAT score in the state from the other variables, and answer the following questions. Present copies of the relevant portions of the R output, and for each question indicate which portion of the output you used and how you used it.

e) Which two states have the greatest effect on the estimated regression line? How would you classify their effect?

f) What subset of independent variables gives the best model for this problem?

g) How would you respond to someone who claimed that the variables not included in the model in part h did not affect the average SAT score of the states?

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