Please help me with this Problem Examine the computation for

Examine the computation formula for r, the sample correlation coefficient. In the formula for r, if we exchange the symbols x and y, do we get a deferent result or do we get the same (equivalent) result? Explain your answer. If we have a set of x and y data values and we exchange corresponding x and y values to get a new data set. should the sample correlation coefficient be the same for both sets of data? Explain your answer. Compute the sample correlation coefficient r for each of the following data sets and show that r n the same for both. (Use 3 decimal places.) In the least-squares line y = 5 - 7x, what is the value of the slope? When x changes by 1 unit, by how much does y change?

Solution

(a) If we exchange the symbols X and Y, The result is same becuase the formula is not depedent on the symbols.

(b) If we a set of X and Y data values and we exchagne corresponding X and Y values to get a new data set, the result is same because the formula is not dependent on which values are the X values and on which values are the y values

(c) (i)

Mean of X = 21 / 3 = 7                  Mean of Y = 11 / 3 = 3.6667       

Var (x) = (155/3) - 7^2 = 2.6667           Var (Y) = (43/3) - (3.6667^2) = 0.88889

Cov(X,Y) = (81/3) - (7*3.6667) =1.3333        r = 0.866

(ii)

Mean of Y = 21 / 3 = 7                  Mean of X = 11 / 3 = 3.6667       

Var (Y) = (155/3) - 7^2 = 2.6667           Var (X) = (43/3) - (3.6667^2) = 0.88889

Cov(X,Y) = (81/3) - (7*3.6667) =1.3333        r = 0.866

(d) Given Y = 5 - 7 X

If X = 1 then Y = -2

if X = 2 then Y = -9

if X = 3 then y = -16

...... . . . . . . . ..

Therefore, when X incresase by 1 unit, Y decrease by 1 units

	X	Y	X^2	Y^2	XY
	7	3	49	9	21
	5	3	25	9	15
	9	5	81	25	45
Total:	21	11	155	43	81