FCAT scores and poverty. In the state of Florida, elementary school performance is based on the average score obtained by students on a standardized exam, called the Florida Comprehensive Assessment Test (FCAT). An analysis of the link between FCAT scores and sociodemographic factors was published in the Journal of Educational
Elementary School | FCAT—Math | FCAT—Reading | % Below Poverty |
1 | 166.4 | 165.0 | 91.7 |
2 | 159.6 | 157.2 | 90.2 |
3 | 159.1 | 164.4 | 86.0 |
4 | 155.5 | 162.4 | 83.9 |
5 | 164.3 | 162.5 | 80.4 |
6 | 169.8 | 164.9 | 76.5 |
7 | 155.7 | 162.0 | 76.0 |
8 | 165.2 | 165.0 | 75.8 |
9 | 175.4 | 173.7 | 75.6 |
10 | 178.1 | 171.0 | 75.0 |
11 | 167.1 | 169.4 | 74.7 |
12 | 177.0 | 172.9 | 63.2 |
13 | 174.2 | 172.7 | 52.9 |
14 | 175.6 | 174.9 | 48.5 |
15 | 170.8 | 174.8 | 39.1 |
16 | 175.1 | 170.1 | 38.4 |
17 | 182.8 | 181.4 | 34.3 |
18 | 180.3 | 180.6 | 30.3 |
19 | 178.8 | 178.0 | 30.3 |
20 | 181.4 | 175.9 | 29.6 |
21 | 182.8 | 181.6 | 26.5 |
22 | 186.1 | 183.8 | 13.8 |
Based on Tekwe, C. D., et al. “An empirical comparison of statistical models for value-added assessment of school performance.” Journal of Educational and Behavioral Statistics , Vol. 29, No. 1, Spring 2004 ( Table ).
and Behavioral Statistics (Spring 2004). Data on average math and reading FCAT scores of third graders, as well as the percentage of students below the poverty level, for a sample of 22 Florida elementary schools are listed in the accompanying table and saved in the FCAT file.
a. Propose a straight-line model relating math score ( y ) to percentage ( x ) of students below the poverty level.
b. Use the method of least squares to fit the model to the data in the FCAT file.
c. Graph the least squares line on a scatterplot of the data. Is there visual evidence of a relationship between the two variables? Is the relationship positive or negative?
d. Interpret the estimates of the y -intercept and slope in the words of the problem.
e. Now consider a model relating reading score ( y ) to percentage ( x ) of students below the poverty level. Repeat parts a–d for this model.
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