The following table shows the mean annual percent return on capital (profitability) and the mean annual percentage sales growth for eight aerospace and defense companies.
Company Profitability Growth
Alliant Techsystems 23.1 8.0
Boeing 13.2 15.6
General Dynamics 24.2 31.2
Honeywell 11.1 2.5
L-3 Communications 10.1 35.4
Northrop Grunmman 10.8 6.0
Rockwell Collins 27.3 8.7
United Technologies 20.1 3.2
a. Compute the correlation coefficient. Conduct a test of hypothesis to determine if it is reasonable to conclude that the population correlation is greater than zero. Use the .05 significance level. Assume growth is the independent variable and profitability is the dependent variable. (Amounts to be deducted should be indicated with minus sign. Round your answers to 3 decimal places.)
X Y X-X Y-Y (X-X)^2 (Y-Y)^2 ((X-X)^2)*((Y-Y)^2)
8.0 23.1 –5.825 5.613 33.931 31.500 -32.693
15.6 13.2 1.775 –4.288 3.151 18.383 -7.610
31.2 24.2 17.375 6.713 301.891 45.058 116.630
2.5 11.1 -11.325 -6.388 128.256 40.800 72.338
35.4 10.1 21.575 -7.388 465.481 54.575 -159.385
6.0 10.8 -7.825 –6.688 61.231 44.723 52.330
8.7 27.3 –5.125 9.813 26.266 96.285 -50.289
3.2 20.1 -10.625 2.613 112.891 6.825 -27.758
110.6 139.9 1133.095 338.149 -36.438
X=_____?
Y=_____?
sx = 12.72
sy = 6.95
r = -.059
H0: ρ ≤ 0; H1: ρ > 0 Reject H0 if t < -1.9432
t =_____?
b. Develop the regression equation for profitability based on growth. Comment on the slope value. (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)
The regression equation is: = ____+ ____ Growth?
c.Which company has the largest residual? (Round your answer to 3 decimal places.)
Rockwell Collins has the largest residual (_____)?
Quick Reply
