Question

1. Using the table below, calculate the variance of X, variance of Y, standard deviation of X, standard deviation of Y,   the covariance between X and Y, the correlation coefficient between X and Y, and find the regression line assuming X is the independent variable (find the slope and the intercept). Show your work

Fill in the Blanks:

X	Y	X-Xbar	Y-Ybar	(X-Xbar)^2	(Y-Ybar)^2	(X-Xbar)*(Y-Ybar)
5	3
9	6
12	15
17	20
21	23
Sum

Calculate the following and show your work.

Xbar:

Ybar:

Variance of X:

Variance of Y:

Standard Deviation of X:

Standard Deviation of Y:   

Covariance between X and Y:

Correlation Coefficient between X and Y:

The Slope of the Regression Line:

The Y Intercept of the Regression Line:   

Regression Line:  

Answer 1

Here in this Question we need to compute the given Statistic based on given sample.

We need to compute the covariance, which is computed by first computing cross products of the sample data.

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	5	3	15	25	9
	9	6	54	81	36
	12	15	180	144	225
	17	20	340	289	400
	21	23	483	441	529
Sum =	64	67	1072	980	1199

Based on the above table, the following is calculated:

1) The sample mean Xbar = 12.8.

2) The sample mean Ybar = 13.4.

3) The Slope of the Regression Line: 1.3333

The Y Intercept of the Regression Line: -3.6667

Regression Line: Yhat = -3.6667 + 1.3333 X.

4) The covariance bet x and y is calculated as below,

The covariance bet x and y is 53.6.

5) The correlation coefficient bt x and y is calculated as below,

The correlation coefficient is 0.974. which is strong positive correlation.

6)the sample Standerd deviation and variance is computed as below,

7) The Variance of x is 40.2.

8) The sample Standerd deviation of X is 6.34.

9) The Variance of Y is 75.3

10) the sample standerd deviation is 8.68.

All above Calculation is done using Statistical software.

Hope it helps.

Thank you.