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# Regression Analysis of NAEP data

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Is the educational achievement level of students related to how much the state in which they reside spends on education? In many communities this important question is being asked by taxpayers who are being asked by their school districts to increase the amount of tax revenue spent on education. In this case, you will be asked to analyze data on state spending and achievement scores in order to determine whether there is any relationship between government spending and student achievement in the public schools.

The federal government?s National Assessment of Educational Progress (NAEP) program is frequently used to measure the educational achievement of students. The Excel spreadsheet: Student Spending Achievement Data and Worksheet 1 (35 states tab) shows the total current spending per pupil per year, and the composite NAEP test score for 35 states that participated in the NAEP program. The composite score is the sum of the math, science, and reading scores on the 1996 (1994 for reading) NAEP test. Pupils tested are in grade 8, except for reading, which is given to fourth-graders only. The maximum possible score is 1300.

The Excel spreadsheet: Student Spending Achievement Data and Worksheet 2 (13 states tab) shows the spending per pupil for 13 states that did not participate in relevant NAEP surveys. These data were reported in an article on spending and achievement level appearing in Forbes (November 3, 1997).

Questions:

a. Develop numerical and graphical summaries of the data.

b. Use regression analysis to investigate the relationship between the amount spent per pupil and the composite score on the NAEP test. Discuss your findings.

c. Do you think that the estimated regression equation developed for these data could be used to estimate the composite scores for the states that did not participate in the NAEP program?

National Assessment of Educational Progress (NAEP) data
State Spending and Student Achievement Scores
for the 35 states that participated

State "Spending
per Pupil (\$)" "Composite
Score"
1 Alabama 3,777 604
2 Arizona 4,041 618
3 Arkansas 4,060 615
4 California 4,917 580
6 Connecticut 7,629 657
7 Delaware 6,208 615
8 Florida 4,934 611
9 Georgia 4,663 611
10 Hawaii 5,532 580
11 Indiana 5,128 649
12 Iowa 5,060 665
13 Kentucky 5,020 626
14 Louisiana 4,049 581
15 Maine 5,561 675
16 Maryland 6,100 625
17 Massachusetts 6,413 658
18 Minnesota 5,477 661
19 Mississippi 3,423 582
20 Missouri 4,483 641
21 Montana 4,985 667
23 New Mexico 4,097 614
24 New York 8,162 628
25 North Carolina 4,521 629
26 North Dakota 4,374 671
27 Rhode Island 6,554 638
28 South Carolina 4,304 603
29 Tennessee 3,800 618
30 Texas 4,520 627
31 Utah 3,280 650
32 Washington 5,338 639
33 West Virginia 5,247 625
34 Wisconsin 6,055 667
35 Wyoming 5,515 657