Question

In: Math

3) The following observations are given for two variables. Y: 5,8,18,20,22,30,10,7 X:2,12,3,6,11,19,18,9 Compute and interpret the...

3) The following observations are given for two variables.

Y: 5,8,18,20,22,30,10,7

X:2,12,3,6,11,19,18,9

Compute and interpret the sample covariance for the above data.

Compute the standard deviation for x.

Compute the standard deviation for y.

Compute and interpret the sample correlation coefficient.

Solutions

Expert Solution

Covariance formula:

N : Sample Size

Y Y- (Y-)2 X X- (X-)2 (X-X)(Y-Y)
5 -10 100 2 -8 64 80
8 -7 49 12 2 4 -14
18 3 9 3 -7 49 -21
20 5 25 6 -4 16 -20
22 7 49 11 1 1 7
30 15 225 19 9 81 135
10 -5 25 18 8 64 -40
7 -8 64 9 -1 1 8
Total =120 =546 =80 =280 =135
Mean =120/8=15 =80/8=10

As the covariance is positive , when Y increases X also increases.

Standard deviation of X

Standard deviation of X = 6.32455532

Standard deviation of Y

Standard deviation of Y = 8.831760866

Sample Correlation : rX,Y

Sample Correlation = 0.345269671

As correlation is positive and less than 0.5 ; which interprets into a weak positive correlation


Related Solutions

Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 8 6 11 14 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 4. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 4. ____to____ c. Using the following equation: Estimate the standard deviation of an individual value...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 8 6 11 14 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3.   to   c. Using the following equation: Estimate the standard deviation of an individual value...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 8 5 11 13 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 4. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 4. to c. Using the following equation: Estimate the standard deviation of an individual value...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 7 5 12 13 Round your answers to two decimal places. A) Using the following equation: Estimate the standard deviation of ŷ* when x = 3. B) Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3. _______to___________ C)   Using the following equation: Estimate the standard deviation of an individual value...
1. Given are five observations for two variables, x and y. x i 1 2 3...
1. Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 3 7 5 12 13 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3. to c. Using the following equation: Estimate the standard deviation of an individual...
Given are five observations for two variables, x and y. x i 1 2 3 4...
Given are five observations for two variables, x and y. x i 1 2 3 4 5 y i 4 7 6 11 13 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3. to c. Using the following equation: Estimate the standard deviation of an individual value...
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 7 11 15 The estimated regression equation for these data is ŷ = 1 + 2.6x. Compute SSE, SST, and SSR using the following equations (to 1 decimal). SSE SST SSR Compute the coefficient of determination r2 (to 3 decimals). Does this least squares line provide a good fit? Compute the sample correlation coefficient (to 4 decimals).
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 3 8 6 11 13 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 4. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 4. to c. Using the following equation: Estimate the standard deviation of an individual value of y...
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 12 14 Round your answers to two decimal places. a. Using the following equation: Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: Develop a 95% confidence interval for the expected value of y when x = 3. to c. Using the following equation: Estimate the standard deviation of an individual value of y...
Given are five observations for two variables, x and y. xi 1 2 3 4 5...
Given are five observations for two variables, x and y. xi 1 2 3 4 5 yi 4 7 6 12 14 a. Using the following equation: 12.32a.jpg Estimate the standard deviation of ŷ* when x = 3. b. Using the following expression: 12.32b.jpg Develop a 95% confidence interval for the expected value of y when x = 3. c. Using the following equation: 12.32c.jpg Estimate the standard deviation of an individual value of y when x = 3. d....
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT