Question

an educational psychologist is writing a report about a study that involved examining the relationship between the score earned on a math test and the score earned on a reading test for a random sample of high school students. scores on both of these tests can range from 300 to 800 points. the educational psychologist finds the correlation between these variables to be 0.69, and she constructs a regression equation in order to predict math test score based on reading test score. the educational psychologist also constructs a scatterplot, as shown below, to be included in the final report. based on this information, which one of the following statements is correct? because math and reading test scores are both in points, r = 0.69 points. the scatterplot was not correctly constructed by the educational psychologist. less than half of the variability in math test score cannot be explained by the regression equation. the regression equation should only be used to predict math test scores for students who earned between 500 and 700 points on the reading test. none of the above statements are correct.

Explanation:

1. Analyze the first option: Correlation coefficient \( r \) is unit - less, so saying \( r = 0.69 \) points is wrong.
2. Analyze the second option: The scatter - plot has math test score on the x - axis and reading test score on the y - axis. There's no rule violated in its construction (e.g., variables are correctly plotted, points are plotted properly), so this statement is wrong.
3. Analyze the third option: The coefficient of determination \( R^{2}=r^{2}=(0.69)^{2}=0.4761\approx0.48 \). This means about 48% of the variability in math test score is explained by the regression equation, so more than half (52%) of the variability is not explained. The statement says "Less than half of the variability in math test score cannot be explained", which is wrong (since more than half is not explained).
4. Analyze the fourth option: The regression equation is based on a sample of high - school students with math scores from 300 - 800. There's no reason to restrict prediction to reading scores between 500 - 700 (the x - axis is math score, y - axis is reading score, and the regression is to predict math from reading, but the range of reading scores in the data is from 300 - 800 as well, and we can use the regression for the range of the data). So this statement is wrong.

Since all the above statements are wrong, the correct option is the one that says "None of the above statements are correct".

Answer:

None of the above statements are correct.