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Regression, Linear Correlation and Scatterplots

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1. Describe in your own words what is meant by "line of best fit."

2. Answer the following:
a. What is the relationship between the sign of the correlation coefficient and the sign of the slope of the regression line?
b. As the value of the correlation coefficient increases from 0 to 1, or decreases from 0 to -1, how do the points of the scatter plot fit the regression line?

3. In your own words, state the primary purpose of:
a. Linear correlation analysis
b. Regression analysis

4. Indicate which would be the independent variable and which would be the dependent variable in each of the following:
a. Blood pressure, Level of activity
b. Crop yield, Rainfall
c. Braking distance, Car speed
d. Internet connection speed, time to download a web page

5. For a particular sample of 50 scores on a psychology exam, the following results were obtained.
First quartile = 67 Third quartile = 91 Standard deviation = 9 Range = 48
Mean = 75 Median = 80 Mode = 81 Midrange = 74
a. What score was earned by more students than any other score? Why?
b. How many students scored between 67 and 91 on the exam?
c. What was the highest score earned on the exam?
d. What was the lowest score earned on the exam?
e. How many students scored within three standard deviations of the mean ?

6. A math test was given with the following results:
70, 46, 82, 71, 48, 30, 99, 72, 80, 85, 42, 60, 39, 86, 47, 68
Find the range, standard deviation, and variance for the scores.

7. Answer the following:
a. What does it mean to say that x = 17 has a standard score of -0.3?
b. What does it mean to say that a particular value of x has a z-score of +5.7?
c. In general, what is the standard score a measure of?

8. A student scored 81 percent on a test, and was in the 67th percentile. Explain these two numbers.
9. An animal trainer obtained the following data (Table A) in a study of reaction times of dogs (in seconds) to a specific stimulus. He then selected another group of dogs that were much older than the first group and measure their reaction times to the same stimulus. The data is shown in Table B.
Table A Table B
Classes Frequency Classes Frequency
2.3-2.9 18 2.3-2.9 4
3.0-3.6 14 3.0-3.6 7
3.7-4.3 11 3.7-4.3 9
4.4-5.0 10 4.4-5.0 22
5.1-5.7 3 5.1-5.7 17
5.8-6.4 2 5.8-6.4 7

Find the variance and standard deviation for the two distributions above. Compare the variation of the data sets. Decide if one data set is more variable than the other.

10. You are given the following data.
Number of Absences Final
Grade
0 97
1 90
2 75
2 82
3 77
3 68
4 60
5 58
6 46
a. Make a scatter plot for the data.
b. Find the correlation coefficient for the data.
c. Find the equation for the regression line for the data, and predict the final grade of a student who misses 3.5 days.

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