26 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

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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Elementary School FCAT Math FCAT-Reading % Below Poverty 18 19 1234567AAAAAAAAA 166.4 165.0 91.7 159.6 157.2 90.2 159.1 164.4 86.0 155.5 162.4 83.9 164.3 162.5 80.4 169.8 164.9 76.5 155.7 162.0 76.0 8 165.2 165.0 75.8 175.4 173.7 75.6 10 178.1 171.0 75.0 11 167.1 169.4 74.7 177.0 172.9 63.2 174.2 172.7 52.9 175.6 174.9 48.5 170.8 174.8 39.1 175.1 170.1 38.4 182.8 181.4 34.3 180.3 180.6 30.3 178.8 178.0 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 2).