The following sample observations were randomly selected ? 13 15 7 12 13 11 XC D
ID: 2949449 • Letter: T
Question
The following sample observations were randomly selected ? 13 15 7 12 13 11 XC Determine the coefficient of correlation and the coefficient of determination. Interpret the association between x and y (Round your coefficient of determination to 4 decimal places. Round all other answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) 5 13 3 15 5.64 19.14 13.14 1.89 5.64 ?. 14 0.30 2.38 4.38 0.02 3.52 1.27 3.52 1.13 -4.08 3 12 4 13 4 11 -0.88 -0.88 1.13 3.13 2.38 0.38 -2.08 -0.33 1.27 9.77 -5.63 -17.58 39 85 x4.875, V=| 10.629 , Sx 1.6579 3.378 0.891Explanation / Answer
Solution;
Correlation coefficiient found using excel as
Given to round of to 2decimals
Correlation coefficient=r=-0.89
coefficient of determiantion = rs=r*r=-0.89081*-0.89081=0.7935
ANSWERS:
xbar:4.88 y bar=10.63 Sx=1.73 Sy=3.34 r=-0.89
the correltion coefficient of -0.89 indicates a very strong negative relationship between x and y.teh coefficient of determiantion is 0.7935 ,found by squaring the value of correlation coefficient.X accounts for 79.35% of the varaition in y
X Y XBAR YBAR X-XBAR Y-YBAR (X-XBAR)^2 (Y-YBAR)^2 (X-XBAR)(Y-YBAR) 5 13 4.875 10.625 0.13 2.38 0.02 5.64 0.30 3 15 4.875 10.625 -1.88 4.38 3.52 19.14 -8.20 6 7 4.875 10.625 1.13 -3.63 1.27 13.14 -4.08 3 12 4.875 10.625 -1.88 1.38 3.52 1.89 -2.58 4 13 4.875 10.625 -0.88 2.38 0.77 5.64 -2.08 4 11 4.875 10.625 -0.88 0.38 0.77 0.14 -0.33 6 9 4.875 10.625 1.13 -1.63 1.27 2.64 -1.83 8 5 4.875 10.625 3.13 -5.63 9.77 31.64 -17.58 TOTAL 0.00 20.88 79.88 -36.38 MEAN 4.88 10.63