Consider n measurements of two variables x and y . Explore the effect that changing the...
Consider n measurements of two variables x and y . Explore the effect that changing the standard deviation of x
has on the correlation between x and y . In particular:
a) Are there ways of increasing the standard deviation and decreasing the magnitude of the correlation? If so,
provide an example.
b) Are there ways of increasing the standard deviation and increasing the magnitude of the correlation? If so, provide
an example.
In either case, you must justify.
Homework Answers
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Consider n measurements of two variables x and y . Explore the
effect that changing the...
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x...
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x = n-ı Σ i , and y = n-ı Σ -1 y be the sample means of the x and y variables. Let & and Sy be the corresponding standard deviations. Let sry and rry be the sample covariance and sample correlation respective . Suppose x = 6.2,J = 8 8 2.95, sy4.494, sy 13.05. Part a) What is the sample correlation of the...
2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b...
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questions.
2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b. (2 pts) Find the standard deviation of X, and standard deviation of Y C. (3 pts) Find the covariance between X and Y d. (2 pts) Find correlation coefficient between X and Y and comment on your answer. 3. The following table shows a random sample of 100 hikers and the areas...
please so it in Two variables X and Y are said to have a spurious correlation...
please so it in
Two variables X and Y are said to have a spurious correlation if their correlation solely reflects each variable's relationship to a third (antecedent) variable Z (and possibly to other variables). The table below presents zero-order correlations based on the responses of 34 subjects. .202 674 430 360 532 Xi .303 X2 Determine the partial correlations ryxI(x2, Tyxix. Exixzy and ryx2x3 b) Test the significance of the partial correlations c) Comment relationships between the variables using...
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean...
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation !5 Y has mean 5 and standard deviation 3. Their correlation is 0.6. What is the mean and standard deviation of X + Y? What is the distribution of X+ Y? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed? Explain your answer.
10. Consider the following scatterplot of two variables X and Y 0.25 020 0.15 0.10 005...
10. Consider the following scatterplot of two variables X and Y 0.25 020 0.15 0.10 005 0.00 00 02 04 06 0S 1.0 We may conclude that the correlation between X and Y: O must be close to -1 because there is nearly a perfect relationship between them, but it is not a straight line relationship. O is close to o. O must be close to 1 because there is nearly a perfect relationship between them. O could be any...
Question 19 Consider two random variables X and Y with E(X)= 4, E(Y) = 2, E(XY)...
Question 19 Consider two random variables X and Y with E(X)= 4, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the correlation coefficient between X and Y is: a. -0.2 b. -0.3 c. 0.2 d. 0.3 e. None of the above need step by step distribution~
4.he sample correlation coefficient between X and Y, rxy Sx/Sx S where S-the covariance between X...
4.he sample correlation coefficient between X and Y, rxy Sx/Sx S where S-the covariance between X and Ys Σ(X-XM) (-Yu)/ n-1 Sx the standard deviation of X and Sy the standard deviation of Y I) If the covariance is positive, the correlation coefficient must be positive: True or False? ii) If the covariance is negative, the correlation coefficient must be positive: True or False? a) ii) The correlation coefficient must lie between 0 and 1. True or False? v)lf the...
Coordinates of the level random vector (X, Y) are random variables whose common distribution is determined...
Coordinates of the level random vector (X, Y) are random variables whose common distribution is determined by probabilities P (X = 6, Y = 9) = 0.3, P (X = 6, Y = −5) = 0.4, P (X = 5, Y = -5) = 0.3. Calculate: (a) The expected value of X and standard deviation (b) The expected value of Y and standard deviation (c) the expected value of the input XY (d) correlation between X and Y
Please consider the following values for the variables X and Y. Treat each row as a...
Please consider the following values for the variables X and Y. Treat each row as a pair of scores for the variables X and Y (with the first row providing the labels "X" and "Y"). X Y 2 4 4 3 6 5 7 7 11 6 Please calculate Pearson's correlation coefficient (r) for these data and report your answer below. When reporting your answer, please provide three decimal places (if relevant).
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
Consider n = 5 pairs (x! ,y, , . . . , (xt, y,'). Let x = n-ı Σ i , and y = n-ı Σ -1 y be the sample means of the x and y variables. Let & and Sy be the corresponding standard deviations. Let sry and rry be the sample covariance and sample correlation respective . Suppose x = 6.2,J = 8 8 2.95, sy4.494, sy 13.05. Part a) What is the sample correlation of the...
please lease solve all
questions.
2. Consider the following two variables X and Y: 4 a. (2 pts) Find the mean of X, and mean of Y b. (2 pts) Find the standard deviation of X, and standard deviation of Y C. (3 pts) Find the covariance between X and Y d. (2 pts) Find correlation coefficient between X and Y and comment on your answer. 3. The following table shows a random sample of 100 hikers and the areas...
please so it in
Two variables X and Y are said to have a spurious correlation if their correlation solely reflects each variable's relationship to a third (antecedent) variable Z (and possibly to other variables). The table below presents zero-order correlations based on the responses of 34 subjects. .202 674 430 360 532 Xi .303 X2 Determine the partial correlations ryxI(x2, Tyxix. Exixzy and ryx2x3 b) Test the significance of the partial correlations c) Comment relationships between the variables using...
10. (5pt) Suppose that X and Y are two normally distributed random variables. X has mean 2 and standard deviation !5 Y has mean 5 and standard deviation 3. Their correlation is 0.6. What is the mean and standard deviation of X + Y? What is the distribution of X+ Y? What if X and Y are jointly normally distributed? What if they are not jointly normally distributed? Explain your answer.
10. Consider the following scatterplot of two variables X and Y 0.25 020 0.15 0.10 005 0.00 00 02 04 06 0S 1.0 We may conclude that the correlation between X and Y: O must be close to -1 because there is nearly a perfect relationship between them, but it is not a straight line relationship. O is close to o. O must be close to 1 because there is nearly a perfect relationship between them. O could be any...
4.he sample correlation coefficient between X and Y, rxy Sx/Sx S where S-the covariance between X and Ys Σ(X-XM) (-Yu)/ n-1 Sx the standard deviation of X and Sy the standard deviation of Y I) If the covariance is positive, the correlation coefficient must be positive: True or False? ii) If the covariance is negative, the correlation coefficient must be positive: True or False? a) ii) The correlation coefficient must lie between 0 and 1. True or False? v)lf the...
5. Suppose X has the Rayleigh density otherwise 0, a. Find the probability density function for Y-X using Theorem 8.1.1. b. Use the result in part (a) to find E() and V(). c. Write an expression to calculate E(Y) from the Rayleigh density using LOTUS. Would this be easier or harder to use than the above approach? of variables in one dimension). Let X be s Y(X), where g is differentiable and strictly incr 1 len the PDF of Y...
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