William H. Knapp III

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This homework was due on Friday, December 7 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. Before we begin, I want to let you know that I'm trying something different for this homework. If you notice the difference, please let me know whether you find it helpful for your learning or not.
What is variance?
A measure indicating the direction of a linear relationship between two variables.
A measure indicating the strength of a linear relationship between two variables.
A measure indicating the strength and direction of a linear relationship between two variables.
A measure of how much a variable varies.
A measure of how much two variables vary together.

2. What is covariance?
A measure indicating the direction of a linear relationship between two variables.
A measure indicating the strength of a linear relationship between two variables.
A measure indicating the strength and direction of a linear relationship between two variables.
A measure of how much a variable varies.
A measure of how much two variables vary together.

3. What is a correlation?
A measure indicating the direction of a linear relationship between two variables.
A measure indicating the strength of a linear relationship between two variables.
A measure indicating the strength and direction of a linear relationship between two variables.
A measure of how much a variable varies.
A measure of how much two variables vary together.

4. The variance of some variable is just the covariance of that variable with itself.
True
False

5. How do you calculate the population covariance between two variables?
Sum the squared differences for both of the variables and divide by the number of pairs.
Sum the squared differences for both of the variables and divide by the number of pairs minus 1.
Sum the squared differences for both of the variables and divide by the total number of observations.
Sum the squared differences for both of the variables and divide by the total number of observations minus 1.
Sum the products of paired differences and divide by the number of pairs.
Sum the products of paired differences and divide by the number of pairs minus 1.
Sum the products of paired differences and divide by the total number of observations.
Sum the products of paired differences and divide by the total number of observations minus 1.

6. How do you estimate the population covariance between two variables from a sample?
Sum the squared differences for both of the variables and divide by the number of pairs.
Sum the squared differences for both of the variables and divide by the number of pairs minus 1.
Sum the squared differences for both of the variables and divide by the total number of observations.
Sum the squared differences for both of the variables and divide by the total number of observations minus 1.
Sum the products of paired differences and divide by the number of pairs.
Sum the products of paired differences and divide by the number of pairs minus 1.
Sum the products of paired differences and divide by the total number of observations.
Sum the products of paired differences and divide by the total number of observations minus 1.

7. How does one calculate the correlation betweeen two variables in a sample? If I don't specifically mention biased or unbiased, you should assume I mean unbiased.
Divide the covariance of the variables by the product of the standard deviations of the variables.
Divide the covariance of the variables by the product of the variances of the variables.
Divide the product of the standard deviations of the variables by the covariance of the variables.
Divide the product of the variances of the variables by the covariance of the variables.

8. What does the product of the standard deviations of two variables indicate?
The correlated portion of the covariance.
The independent portion of the covariance.
The maximum amount that two variables with those standard deviations could covary.
The minimum amount that two variables with those standard deviations could covary.

9. What does it mean when the correlation coefficient equals 1?
There is a perfect linear relationship between the variables.
There is an imperfect linear relationship between the variables.
There is no linear relationship between the variables.
There is no relationship between the variables.

10. What does it mean when the correlation coefficient equals -.47?
There is a perfect linear relationship between the variables.
There is an imperfect linear relationship between the variables.
There is no linear relationship between the variables.
There is no relationship between the variables.

11. What does it mean when the correlation coefficient equals -1?
There is a perfect linear relationship between the variables.
There is an imperfect linear relationship between the variables.
There is no linear relationship between the variables.
There is no relationship between the variables.

12. What does it mean when the correlation coefficient equals 0?
There is a perfect linear relationship between the variables.
There is an imperfect linear relationship between the variables.
There is no linear relationship between the variables.
There is no relationship between the variables.

13. What does it mean when the sign of the correlation coefficient is positive? Choose all that apply.
Decreases in one variable are generally associated with decreases in the other.
Decreases in one variable are generally associated with increases in the other.
Decreases in one variable are not generally associated with increases or decreases in the other.
Increases in one variable are generally associated with decreases in the other.
Increases in one variable are generally associated with increases in the other.
Increases in one variable are not generally associated with increases or decreases in the other.

14. What does it mean when the sign of the correlation coefficient is negative? Choose all that apply.
Decreases in one variable are generally associated with decreases in the other.
Decreases in one variable are generally associated with increases in the other.
Decreases in one variable are not generally associated with increases or decreases in the other.
Increases in one variable are generally associated with decreases in the other.
Increases in one variable are generally associated with increases in the other.
Increases in one variable are not generally associated with increases or decreases in the other.

15. What does it mean when two variables vary independently of one another? Choose all that apply.
Decreases in one variable are generally associated with decreases in the other.
Decreases in one variable are generally associated with increases in the other.
Decreases in one variable are not generally associated with increases or decreases in the other.
Increases in one variable are generally associated with decreases in the other.
Increases in one variable are generally associated with increases in the other.
Increases in one variable are not generally associated with increases or decreases in the other.

16. Imagine that the covariance of two varaibles was 10 and that the standard deviations of the two variables were 2 and 5. What would the correlation between the variables be?

17. Imagine that the covariance of two varaibles was -6 and that the standard deviations of the two variables were 3 and 8. What would the correlation between the variables be?

18. Please copy and paste the following to use as data for the next 3 questions.
someiv=c(5,8,12,6,3,9,5,4,11,7)
somedv=c(9,6,8,10,12,4,8,10,6,7)
What is the covariance between these two variables?

19. What's the correlation between the two variables from the above question?

20. Please copy and paste the following code which will sort the data from the previous variables into ascending order.
somenewiv=sort(someiv)
somenewdv=sort(somedv)
What is the correlation between these new variables?