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Correlation Coefficients and Regressions

Use the following information to answer questions 1-3:
Row 1 | 5 6 5 8 5 3 9 11 10 9
Row 2 | -5.0 -4.0 -3.5 -4.1 -2.4 -2.0 -5.0 -7.2 -5.6 -6.4
1. Using row 1 of the table above for the x-values and row 2 for the y-values, find the value of
the correlation coefficient, r.
2. Using row 2 of the table above for the x-values and row 1 for the y-values, find the value of
the correlation coefficient, r.
3. What do you conclude from the results for problems 1 and 2?

Use the table below to answer questions 4-8. The table shows the ages of 13 electrical engineers
and the annual salaries (in thousands of dollars).
Age, x | 22 25 29 34 39 43 48 53 56 61 64 67 69
Salary, y | 54 57 61 65 69 72 74 74 79 79 82 89 89
4. What is the correlation coefficient, r?
5. What can we conclude from the value of r?
6. What is the regression equation?
7. If possible, predict the salary for a 45 year old electrical engineer.
8. if possible predict the salary for 72 year old engineer.

Use the following information to answer questions 12-14:
Blood Types The probability that a person in the United States has type O+ blood is 32%.
Three unrelated people in the United States are selected at random.
12. Find the probability that all three have type O+ blood.
13. Find the probability that none of the three has type O+ type blood.
14. Find the probability that at least one of the three has type O+ type blood.

Use the following information to answer questions 15-17:
Bookbinding Defects A printing company's bookbinding machine has a probability of 0:003
of producing a defective book. The machine is used to bind 3 books.
15. Find the probability that none of the books is defective.
16. Find the probability that at least one of the books is defective.
17. Find the probability that all of the books are defective.

Use the following information to answer questions 18 and 19:
Birthdays Four people are selected at random. Assume 365 days in a year.
18. What is the probability that all four share the same birthday?
19. What is the probability that none of the four shares the same birthday?

Solution Preview

Use the following information to answer questions 1-3.
Row 1 5 6 5 8 5 3 9 11 10 9
Row 2 -5.0 -4.0 -3.5 -4.1 -2.4 -2.0 -5.0 -7.2 -5.6 -6.4
1. Using row 1 of the table above for the x-values and row 2 for the y-values, find the value of
the correlation coefficient, r.
x y µx µ y (x-µx)^2 (y-µ y)^2 (x-µx)*(y-µy)
1 2 6.545 -3.9273 30.747025 35.13289 -32.8668785
5 -5 2.387025 1.150685 1.6573215
6 -4 0.297025 0.005285 0.0396215
5 -3.5 2.387025 0.182585 -0.6601785
8 -4.1 2.117025 0.029825 -0.2512785
5 -2.4 2.387025 2.332645 -2.3596785
3 -2 12.567025 3.714485 -6.8322785
9 -5 6.027025 1.150685 -2.6334785
11 -7.2 19.847025 10.71057 -14.5798785
10 -5.6 11.937025 2.797925 -5.7791785
9 -6.4 6.027025 6.114245 -6.0704785
8.793388636 5.756529 -6.394214864 sum

r=Sxy/sqrt(Sxx*Syy)=-6.394214864/sqrt(8.793388636*5.756529)=-0.8987
2. Using row 2 of the table above for the x-values and row 1 for the y-values, find the value of
the correlation coefficient, r.
y x µy µ x (y-µy)^2 (x-µ ...

Solution Summary

This solution answers many questions regarding correlation coefficients, values of r and probability.

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