Review the following concepts if necessary:

- Scatterplots for AP Statistics
- Correlation for AP Statistics
- Lines of Best Fit for AP Statistics
- Residuals for AP Statistics
- Coefficient of Determination for AP Statistics
- Outliers and Influential Observations for AP Statistics
- Transformations to Achieve Linearity for AP Statistics

### Rapid Review

*Answer:* There is a strong, positive, linear association between *x* and *y*. That is, as one of the variables increases, the other variable increases as well.

*Answer:* The residual plot shows a definite pattern. If a line was a good model, we would expect to see a more or less random pattern of points about 0. A line is unlikely to be a good model for this data.

*Answer:* A is an *outlier* because it is removed from the general pattern of the rest of the points. It is an *influential observation* since its removal would have an effect on a calculation, specifically the slope of the regression line. Removing A would increase the slope of the LSRL.

*Answer:* For each additional hour studied, the *GPA* is predicted to increase by 0.11. Alternatively, you could say that the *GPA* will increase 0.11 on average for each additional hour studied.

*Answer:* *r*^{2} = 0.45 means that 45% of the variability in college *GPA* is explained by the regression of *GPA* on socioeconomic status.

*Answer:* Correlation is not causation. The crime rate could have gone down for a number of reasons besides Governor Jones's efforts.

*Answer:* *weight* = –104.64 + 3.4715(*height*); *r* = =0.921. r is positive since the slope of the regression line is positive and both must have the same sign.

*Answer:* The standard error of the slope of the regression line is 0.5990. It is an estimate of the change in the mean response *y* as the independent variable *x* changes. The standard error of the residuals is s = 7.936 and is an estimate of the variability of the response variable about the LSRL.

- The correlation between two variables
*x*and*y*is 0.85. Interpret this statement. - The following is a residual plot of a least-squares regression. Does it appear that a line is a good model for the data? Explain.
- Consider the following scatterplot. Is the point A an outlier, an influential observation, or both? What effect would its removal have on the slope of the regression line?
- A researcher finds that the LSRL for predicting
*GPA*based on average hours studied per week is*GPA*= 1.75 + 0.11 (hours studied ). Interpret the slope of the regression line in the context of the problem. - One of the variables that is related to college success (as measured by
*GPA*) is socioeconomic status. In one study of the relationship,*r*^{2}= 0.45. Explain what this means in the context of the problem. - Each year of Governor Jones's tenure, the crime rate has decreased in a linear fashion. In fact,
*r*= –0.8. It appears that the governor has been effective in reducing the crime rate. Comment. - What is the regression equation for predicting weight from height in the following computer printout and what is the correlation between height and weight?
- In the computer output for Exercise #7 above, identify the standard error of the slope of the regression line and the standard error of the residuals. Briefly explain the meaning of each.

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