Question

I have absolutely no idea where to start with this or even how to do it. The chart is what is throwing me off. I just need to know how to do this problem, how to start it, and how does the chart even relate to the problem? For variance, you need a mean I guess, how is that possible with the chart?

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.

X	Y	X-Xbar	Y-Ybar	(X-Xbar)^2	(Y-Ybar)^2	(X-Xbar)*(Y-Ybar)
3	1
8	5
10	13
15	18
19	23

Answer 1

X	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
3 8 10 15 19	1 5 13 18 23	64.000 9.000 1.000 16.000 64.000 Sum: 154.000	121.000 49.000 1.000 36.000 121.000 Sum: 328.000	88.000 21.000 -1.000 24.000 88.000 Sum: 220.000

Varx = . = 154/5 = 30.8

Vary = . = 328/5 = 65.6

S.D (x) = √var(x) = 5.55

S.D (y) = √vary = 8.09

Cov(x,y) = 220/5 = 44

Correlation coefficient r = cov(x,y)/(S.Dx)×(S.Dy)

= 44/(5.55×8.09) = 0.98

Regression equation

Y^ = a+bx

b = r×sy/sx

0.98×8.09/5.55 = 1.428

a = ybar - b×xbar = 12-11×1.428 = - 3.708

So y ^ = -3.708+ 1.428x