III.A definite pattern in the residual plot is an indication that a nonstraight model will certainly display a better fit to the data than the right regression line.

You are watching: Suppose the correlation between two variables is r=0.23

2. Documents are derived for a team of college freshmen examining their SAT scores (math plus composing plus important reading) from their senior year of high school and also their GPAs in the time of their first year of college. The resulting regression equation is

= 0.55 + 0.00161 (SAT total) through r = 0.632

What percentage of the variation in GPAs have the right to be explained by looking at the straight partnership between GPAs and SAT scores?

3. In a study of whether the structure of the adult human brain alters once a new skill is learned, the gray matter volume of four people was measured before and after learning a new cognitive ability. The resulting scatterplot was:


The correlation over is 0. Three researchers each run the experiment on a new topic and also each achieve an additional information point:


Match the above scatterplots with their brand-new correlations.






4. In a research of winning portion in residence games versus average home attendance for expert baseround teams, the resulting regression line is:


What is the residual if a team has a winning percent of 55% via an average attendance of 34,000?

5. Consider the complying with scatterplot of midterm and also final exam scores for a class of 15 students.


Which of the adhering to is incorrect?

6. If eincredibly womale married a man who was precisely 2 inches taller than she, what would the correlation between the heights of married men and woguys be?

7. Suppose the correlation between two variables is r = 0.23. What will the brand-new correlation be if 0.14 is added to all values of the x-variable, eextremely worth of the y-variable is doubled, and the two variables are interchanged?

8. Suppose the correlation in between two variables is -0.57. If each of the y-scores is multiplied by -1, which of the following is true around the new scatterplot?

9. Consider the set of points (2, 5), (3, 7), (4, 9), (5, 12), (10, n). What must n be so that the correlation in between the x- and y-values is 1?

11. Consider the 3 points (2, 11), (3, 17), and (4, 29). Given any right line, we have the right to calculate the amount of the squares of the three vertical distances from these points to the line. What is the smallest feasible worth this sum have the right to be?

12. Suppose that the scatterplot of log X and log Y mirrors a strong positive correlation close to 1. Which of the complying with is true?


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Consider n pairs of numbers. Suppose

= 2, sx = 3,
= 4, and also sy = 5. Of the complying with, which might be the least squares line?

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