Question: The SAT is a test often used
The SAT is a test often used as part of an application to college. SAT scores are between 200 and 800, but have no units. Tests are given in both Math and Verbal areas. SAT-Math problems require the ability to read and understand the questions, but can a person verbal score be used to predict the math score? Verbal and math SAT scores of a high school graduating class are displayed in the scatterplot, with the regression line added.
1. Describe the relationship.
2. Are there any students whose scores do not seem to fit the overall pattern?
3. For these data, r=0.685. Interpret this statistic.
4. These verbal scores averaged 596.3, with a standard deviation of 99.5, and the math scores averaged 612.1, with a standard deviation of 98.1. Write the equation of the regression line predicting math scores from verbal scores.
5. Interpret the slope of this line.
6. Predict the math score of a student with a verbal score of 500.
7. Every year, some students score a perfect 1600 (800 on both tests). Based on this model, what would such a student residual be for her math score?
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> Consider the Albuquerque home sales from Exercise 29 again. The regression analysis gives the model Price=47.82+0.061Â Size. 1. Explain what the slope of the line says about housing prices and house size. 2. What price would you predict for a 3000-square
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> The regression of Price on Size of homes in Albuquerque had R2=71.4%, as described in Exercise 29. Write a sentence (in context, of course) summarizing what the R2 says about this regression.
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> If you create a regression model for predicting the Weight of a car (in pounds) from its Length (in feet), is the slope most likely to be 3, 30, 300, or 3000? Explain.
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> Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data.
> A candidate for office claims that there is a correlation between television watching and crime. Criticize this statement on statistical grounds.
> Tell what each of the residual plots below indicates about the appropriateness of the linear model that was fit to the data.
> Fill in the missing information in the following table.
> Fill in the missing information in the following table.
> For Exercise 16 regression model predicting fuel economy (in mpg) from the car engine size, se=3.522. Explain in this context what that means.
> For Exercise 15 regression model predicting potassium content (in milligrams) from the amount of fiber (in grams) in breakfast cereals, se=30.77. Explain in this context what that means.
> The correlation between a car engine size and its fuel economy (in mpg) is r=0.774. What fraction of the variability in fuel economy is accounted for by the engine size?
> The correlation between a cereal fiber and potassium contents is r=0.903. What fraction of the variability in potassium is accounted for by the amount of fiber that servings contain?
> In Exercise 16, the regression model Combined MPG=33.46 3.23 Displacement relates cars engine size to their fuel economy (Combined mpg). Explain what the slope means.
> In Exercise 15, the regression model Potassium^=38+27 Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of breakfast cereals. Explain what the slope means.
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