Question

The accompanying data represent the total compensation for 12 randomly selected chief executive officers (CEO) and the company's stock performance in a recent year. Complete parts (a) through (d) below. Click the icon to view the CEO data. (a) One would think that a higher stock return would lead to a higher compensation. Based on this, what would likely be the explanatory variable? Stock return Compensation (b) Draw a scatter diagram of the data. Use the result from part (a) to determine the explanatory variable. Choose the correct graph below. O A B. OD 160 160- Q 25 Stock Return Stock Return . Compensation 10 0+ 0 Compensation O D 160 Stock Return 160 Compensation Stock Return (c) Determine the linear correlation coefficient between compensation and stock return ra (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer 1 part remaining Clear All Check AS

Answer 1

X Values 14.56 4.12 7.06 1.07 1.93 3.78 12.06 7.55 8.47 4.07 20.87 6.67 Y Values 75.43 64.02 142.03 32.75 10.64 30.66 0.74 69.41 58.68 55.94 24.26 32.23 Y Values X Values X - My Y - My 6.876 -3.564 -0.624 -6.614 -5.754 -3.904 4.376 -0.134 0.786 -3.614 13.186 -1.014 25.697 14.287 92.297 -16.983 -39.093 -19.073 -48.993 19.677 8.947 6.207 -25.473 -17.503 (X - My)2 47.277 12.703 0.390 43. 747 33.110 15.243 19.148 0.018 0.618 13.062 173.866 1.029 (Y - My)2 660.362 204.133 8518.829 288.405 1528.224 363.760 2400.265 387.204 80.058 38.533 648.848 306.338 (X - Mx)(Y - My) 176.692 -50.923 -57.609 112.325 224.945 74.462 -214.383 -2.640 7.031 -22.435 -335.876 17.750 Mx: 7.684 My: 49.733 Sum: 360.210 Sum: 15424.957 Sum: -70.661

Result Details & Calculation

X Values

∑ = 92.21

Mean = 7.684

∑(X - Mx)2 = SSx = 360.21

Y Values

∑ = 596.79

Mean = 49.733

∑(Y - My)2 = SSy = 15424.957

X and Y Combined

N = 12

∑(X - Mx)(Y - My) = -70.661

R Calculation

r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -70.661 / √((360.21)(15424.957)) = -0.03

Meta Numerics (cross-check)

r = -0.03

b)

Y Values X Values 3565 3340 3475 2655 3300 20 21 20 26 23 Y Values X Values Y - My X - My 298.000 73.000 208.000 -612.000 33.000 -2.000 -1.000 -2.000 4.000 1.000 (X - Mx)2 88804.000 5329.000 43264.000 374544.000 1089.000 (Y - My)? 4.000 1.000 4.000 16.000 1.000 (X - MX)(Y - My) -596.000 -73.000 -416.000 -2448.000 33.000 Mx: 3267.000 My: 22.000 Sum: 26.000 Sum: -3500.000 Sum: 513030.000

Result Details & Calculation

X Values
∑ = 16335
Mean = 3267
∑(X - Mx)2 = SSx = 513030

Y Values
∑ = 110
Mean = 22
∑(Y - My)2 = SSy = 26

X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -3500

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -3500 / √((513030)(26)) = -0.9583

Meta Numerics (cross-check)
r = -0.9583