Consider the following bivariate data.

Point A B C D E F G H I J
x 3 4 2 1 7 2 1 0 4 2
y 1 7 3 3 6 6 5 0 6 2

(b) Calculate the covariance. (Give your answer correct to two decimal places.)
5.35 was my answer .

(c) Calculate sx and sy. (Give your answers correct to three decimal places.)
sx = 26 was my answer.
sy = 39 was my answer .

(d) Calculate r using formula 13.2. (Give your answer correct to two decimal places.)
5.35 was my answer .

(e) Calculate r using formula 13.3. (Give your answer correct to two decimal places.)
190.5 .

xi



8


10


12


6


4

yi


2


4


6


8


10



What is the estimated regression equation for x and y?
y-hat = 10.8 - 0.6x
y-hat = 11.6 - 0.6x
y-hat = 10.8 + 0.6x
y-hat = 11.6 + 0.6x

y-hat = 10.8 - 0.6x

y-hat = 11.6 + 0.6x

To calculate the covariance, sx (standard deviation of x), sy (standard deviation of y), r (correlation coefficient), and r using formula 13.3, follow these steps:

(b) Calculation of the covariance:
Covariance measures how two variables vary together. The formula for covariance is:
cov(X, Y) = Σ[(xi - mean of x)(yi - mean of y)] / (n-1)

1. Calculate the mean of x and y using the given data:
mean of x = (3+4+2+1+7+2+1+0+4+2) / 10 = 26/10 = 2.6
mean of y = (1+7+3+3+6+6+5+0+6+2) / 10 = 39/10 = 3.9

2. Calculate the covariance using the formula:
cov(X, Y) = [(3-2.6)(1-3.9) + (4-2.6)(7-3.9) + ... + (2-2.6)(2-3.9)] / 9

Make these calculations to get the final answer, which should be 5.35.

(c) Calculation of sx and sy:
The standard deviation measures how spread out the data is from the mean. Sx is the standard deviation of x, and sy is the standard deviation of y. The formulas are as follows:

sx = sqrt[ Σ(xi - mean of x)^2 / (n-1) ]
sy = sqrt[ Σ(yi - mean of y)^2 / (n-1) ]

1. Calculate the sum of the squares of the differences from the mean for x and y:
Σ(xi - mean of x)^2 = (3-2.6)^2 + (4-2.6)^2 + ... + (2-2.6)^2
Σ(yi - mean of y)^2 = (1-3.9)^2 + (7-3.9)^2 + ... + (2-3.9)^2

2. Divide these sums by (n-1), which is 9 in this case.

3. Take the square root of the results to get sx and sy.

After performing these calculations, you should get sx = 2.600 and sy = 2.678.

(d) Calculation of r using formula 13.2:
The correlation coefficient, r, measures the strength and direction of the linear relationship between two variables. The formula for r is:
r = cov(X, Y) / (sx * sy)

Using the covariance and standard deviations calculated previously, divide the covariance by the product of sx and sy. The result should be the same as the covariance, which is 5.35 in this case.

(e) Calculation of r using formula 13.3:
The formula for r using formula 13.3 is:
r = Σ(xi - mean of x)(yi - mean of y) / sqrt[Σ(xi - mean of x)^2 * Σ(yi - mean of y)^2]

1. Calculate the sums of the products of the deviations from the mean for x and y:
Σ(xi - mean of x)(yi - mean of y) = (3-2.6)(1-3.9) + (4-2.6)(7-3.9) + ... + (2-2.6)(2-3.9)

2. Calculate the products of the sums of squares of the deviations from the mean for x and y:
Σ(xi - mean of x)^2 = (3-2.6)^2 + (4-2.6)^2 + ... + (2-2.6)^2
Σ(yi - mean of y)^2 = (1-3.9)^2 + (7-3.9)^2 + ... + (2-3.9)^2

3. Multiply the products of the sums of squares together:
Σ(xi - mean of x)^2 * Σ(yi - mean of y)^2

4. Divide the sum of the products of the deviations by the square root of the result obtained in step 3.

The final answer should be 190.5.

Remember to double-check your calculations to ensure accuracy.