Airlines have increasingly outsourced the maintenance of their planes to other c

ID: 3170687 • Letter: A

Question

Airlines have increasingly outsourced the maintenance of their planes to other companies. Critics say that the maintenance may be less carefully done, so that outsourcing creates a safety hazard. As evidence, they point to government data on percent of major maintenance outsourced and percent of flight delays blamed on the airline (often due to maintenance problems). (Data set may be found here.)

(b) Find the correlation r with and without Hawaiian Airlines. (Round your answers to three decimal places.)

(c) Find the least-squares lines for predicting delay percent from outsourcing percent with and without Hawaiian Airlines. (Enter your intercepts to two decimal places, and your slopes to five decimal places.)

Use the line from above that includes Hawaiian Airlines to predict the percent of delays blamed on an airline that has outsourced 79.1% of its major maintenance. (Round your answer to two decimal places.)
%

Give the predicted percent with Hawaiian Airlines removed. (Round your answer to two decimal places.)
%

with Hawaiian Airlines r = without Hawaiian Airlines r = Airline Alaska American Delta Frontier Hawaiian outsource Delay Percent Airline Percent 52.1 10.51 JetBlue 20.41 25.7 Southwest 41.3 12.46 United 19.80 US Airways 0.1 79.1 4.85 Outsource Delay Percent Percent 19.60 66.3 19.58 60.8 47.3 23.17 10.80 56.5

Explanation / Answer

(b) Find the correlation r with and without Hawaiian Airlines. (Round your answers to three decimal places.)

with Hawaiian Airlines

r( X,Y) =Co V ( X,Y) / S.D (X) * S.D (y)
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )

Co v ( X, Y ) = 1 /9 (6168.406) - [ 1/9 *429.2 ] [ 1/9 *141.18] = -62.701
S. D ( X ) = Sqrt( 1/9*24859.28-(1/9*429.2)^2) = 22.089
S .D (Y) = Sqrt( 1/9*2518.8676-(1/9*141.18)^2) = 5.814
r(x,y) = -62.701 / 22.089*5.814 = -0.4882

ii. without Hawaiian Airlines

r( X,Y) =Co V ( X,Y) / S.D (X) * S.D (y)
r( X,Y) = Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )

Co v ( X, Y ) = 1 /8 (5784.771) - [ 1/8 *350.1 ] [ 1/8 *136.33] = -22.671
S. D ( X ) = Sqrt( 1/8*18602.47-(1/8*350.1)^2) = 20.252
S .D (Y) = Sqrt( 1/8*2495.3451-(1/8*136.33)^2) = 4.638
r(x,y) = -22.671 / 20.252*4.638 = -0.2414

Mean of X = X / n =    47.6889
Mean of Y = Y / n =   15.6867
(Xi - Mean)^2 =   4391.2087
(Yi - Mean)^2 =   304.22
(Xi-Mean)*(Yi-Mean) =   -564.3114
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2
b1 = -564.3114 / 4391.2087 = -0.1285
bo = Y / n - b1 * X / n
bo = 15.6867 - -0.1285*47.6889 = 21.8152

Y = bo + b1 X

Y'=21.8152-0.1285*X

Without Hawaiian Airlines y = + x

( X) ( Y) X^2 Y^2 X*Y 52.1 10.51 2714.41 110.4601 547.571 25.7 20.41 660.49 416.5681 524.537 41.3 12.46 1705.69 155.2516 514.598 0.1 19.8 0.01 392.04 1.98 79.1 4.85 6256.81 23.5225 383.635 66.3 19.6 4395.69 384.16 1299.48 60.8 19.58 3696.64 383.3764 1190.464 47.3 23.17 2237.29 536.8489 1095.941 56.5 10.8 3192.25 116.64 610.2 429.2 141.18 24859.28 2518.8676 6168.406 = TOTALS

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