Question

In: Statistics and Probability

Calculate the covariance between variables X and Y. Is it a positive or negative relationship between...

Calculate the covariance between variables X and Y. Is it a positive or negative relationship between the two variables?

b. Calculate correlation coefficient between X and Y. Is it a positive or negative relationship? Is it a strong linear, weak linear or nonlinear relationship between X and Y?

c. Use the Y data to calculate mean, range, standard deviation and variance.

d. Use the first Y value to calculate the Z-score. Is it an outlier?

e. Calculate the 60th percentile for the Y data.

1	-22	22
2	-33	49
3	2	8
4	29	-16
5	-13	10
6	21	-28
7	-13	27
8	-23	35
9	14	-5
10	3	-3
11	-37	48
12	34	-29
13	9	-18
14	-33	31
15	20	-16
16	-3	14
17	-15	18
18	12	17
19	-20	-11
20	-7	-22

Solutions

Expert Solution

Let us first calculate the covariance between X and Y. This is calculated with the formula:

where are means of x and y values.

First we form a table as below for further calculations.

	X	Y	X^2	Y^2	XY
	-22	22	484	484	-484
	-33	49	1089	2401	-1617
	2	8	4	64	16
	29	-16	841	256	-464
	-13	10	169	100	-130
	21	-28	441	784	-588
	-13	27	169	729	-351
	-23	35	529	1225	-805
	14	-5	196	25	-70
	3	-3	9	9	-9
	-37	48	1369	2304	-1776
	34	-29	1156	841	-986
	9	-18	81	324	-162
	-33	31	1089	961	-1023
	20	-16	400	256	-320
	-3	14	9	196	-42
	-15	18	225	324	-270
	12	17	144	289	204
	-20	-11	400	121	220
	-7	-22	49	484	154
Total	-75	131	8853	12177	-8503

From the data, we have n=20

Now

Since the Covaraiance is negative, the relationship between X and Y is negative.

b). To find out the linear relationship between X and Y, we use the formula.

. Since the Correlation coefficient is -0.8134, it is a negative relationship between X and Y. Since the Value is more than 0.75, it is a string negative linear relationship.

c). For the Y data,

The mean

Variance

Therefore the sample variance of Y is

The range is Maximum-minimum of all values

d). Z score for first value of Y ie 22

The Z score is given by:

Since we have calculated , s=24.4077

. It doesn't seem to be an outlier.

e). To calculate, 60th percentile, we need to order the data in ascending order and locate the 20*60/100 th value.

ie 12th value. The sorted data is presented below:

-29
-28
-22
-18
-16
-16
-11
-5
-3
8
10
14
17
18
22
27
31
35
48
49

The 12th value in the sorted data is the 60th percentile which is 14.

orchestra answered 11 months ago

Next > < Previous

Related Solutions

a. Calculate the covariance between variables X and Y. Is it a positive or negative relationship between the two variables?

Observation x y 1 -22 22 2 -33 49 3 2 8 4 29 -16 5 -13 10 6 21 -28 7 -13 27 8 -23 35 9 14 -5 10 3 -3 11 -37 48 12 34 -29 13 9 -18 14 -33 31 15 20 -16 16 -3 14 17 -15 18 18 12 17 19 -20 -11 20 -7 -22 Answer the following questions a. Calculate the covariance between variables X and Y. Is it a positive...

Let X and Y be random variables with means µX and µY . The covariance of...

Let X and Y be random variables with means µX and µY . The covariance of X and Y is given by, Cov(X, Y ) = E[(X − µX)(Y − µY )] a) Prove the following three equalities: Cov(X, Y ) = E[(X − µX)Y ] = E[X(Y − µY )] = E(XY ) − µXµY b) Suppose that E(Y |X) = E(Y ). Show that Cov(X, Y ) = 0 (hint: use the law of interated expectations to show...

2. Theory gives you the following relationship between variables x and y, y = β0 +...

2. Theory gives you the following relationship between variables x and y, y = β0 + β1x + u. You collect a sample of data on n = 4 sample members. The data are : {x1, y1} = {3, 8},{x2, y2} = {2, 7},{x3, y3} = {1, 6},{x4, y4} = {3, 4} a. State the minimization problem that you need to derive the OLS estimators b. Estimate the relationship between x and y using this sample. What is your estimate...

Think of a pair of variables that has a strong linear relationship, either positive or negative,...

Think of a pair of variables that has a strong linear relationship, either positive or negative, then find data that you think supports your assertion. You need to get real data for this problem, not just make numbers up to fit your hypothesis.

Explain the difference between a positive linear relationship, a negative linear relationship, and a nonlinear relationship...

Explain the difference between a positive linear relationship, a negative linear relationship, and a nonlinear relationship and give an example of each.

Fourth Question: The table below represents a relationship between two variables X and Y x 7,8,4,3,9,5,7,1,2...

Fourth Question: The table below represents a relationship between two variables X and Y x 7,8,4,3,9,5,7,1,2 y 8,10,5,2,12,3,9,1,1 a) Calculate the Pearson correlation coefficient between the X and Y variables. B) Find the y regression equation for X for the cooked data c) Calculate the estimated value (prediction) of the variable Y when the value of the variable X is equal to 5. What is the error value of the estimate?

Put a + if the relationship is positive; put a - if the relationship is negative....

Put a + if the relationship is positive; put a - if the relationship is negative. If there is no relationship, write NC. If an account payable is paid-off with cash, net working capital _________. If cash dividends are paid, retained earnings _________ and total assets ________. If an account payable is refinanced with a short-term bank loan, net working capital ________and inventory turnover ________. If the yield curve is positively sloped and long-term debt is substituted for short-term debt,...

Put a + if the relationship is positive; put a - if the relationship is negative....

Put a + if the relationship is positive; put a - if the relationship is negative. If there is no relationship, write NC. Paying accounts payable faster _______________ the firm’s need for funds. Retiring commercial paper ___________ net working capital ___________ the debt ratio, and ___________ fixed asset turnover. When a firm issues subordinated bonds, retained earnings ________ and the debt ratio ________. The sale of a fixed asset for cash _________ accounts payable. __________ days sales outstanding, and _______________ the current...

Contract the scatter plot of these data. Describe relationship between x and y. What type of relationship appears to exist between two variables?

Use the following data: x y 10 3 6 7 9 3 3 8 2 9 8 5 3 7 Contract the scatter plot of these data. Describe relationship between x and y. What type of relationship appears to exist between two variables? (you can copy and past from Excel,SAS,etc) Compute the correlation coefficient r. Test to determine whether the population correlation coefficient is positive. Use the α=0.01 level to conduct test. (calculate test statistics and make conclusion)

The relationship between income and saving is ( direct, inverse; positive, negative ). That means, as...

The relationship between income and saving is ( direct, inverse; positive, negative ). That means, as income increases, the amount of saving ( increases, decreases, stays the same ). What is the slope of the line? Slope = ________ = Vertical changes ÷ Horizontal changes The slope shows the amount of changes in savings due to the changes in income. That is, for every $1 increase in income, the amount of increase in saving will be $_____. The vertical intercept?...

Subjects

1	-22	22
2	-33	49
3	2	8
4	29	-16
5	-13	10
6	21	-28
7	-13	27
8	-23	35
9	14	-5
10	3	-3
11	-37	48
12	34	-29
13	9	-18
14	-33	31
15	20	-16
16	-3	14
17	-15	18
18	12	17
19	-20	-11
20	-7	-22

1	-22	22
2	-33	49
3	2	8
4	29	-16
5	-13	10
6	21	-28
7	-13	27
8	-23	35
9	14	-5
10	3	-3
11	-37	48
12	34	-29
13	9	-18
14	-33	31
15	20	-16
16	-3	14
17	-15	18
18	12	17
19	-20	-11
20	-7	-22

1	-22	22
2	-33	49
3	2	8
4	29	-16
5	-13	10
6	21	-28
7	-13	27
8	-23	35
9	14	-5
10	3	-3
11	-37	48
12	34	-29
13	9	-18
14	-33	31
15	20	-16
16	-3	14
17	-15	18
18	12	17
19	-20	-11
20	-7	-22