Q 65. Outsourcing by airlines Exercise... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 3: Q 65. (page 195)

Outsourcing by airlines Exercise $5$ (page $158$ ) gives data for $14$ airlines on the percent of major maintenance outsourced and the percent of flight delays blamed on the airline.
(a) Make a scatterplot with outsourcing percent as $x$ and delay percent as $y$ Hawaiian Airlines is a high outlier in the $y -$ direction. Because several other airlines have similar values of $x$ the influence of this outlier is unclear without actual calculation.
(b) Find the correlation $r$ with and without Hawaiian Airlines. How influential is the outlier for correlation?
(c) Find the least-squares line for predicting $y$ from $x$ with and without Hawaiian Airlines. Draw both lines on your scatterplot. Use both lines to predict the percent of delays blamed on an airline that has outsourced $76 %$ of its major maintenance. How influential is the outlier for the least-squares line?

Short Answer

Expert verified

Part (b) $r (w i t h H a w a i i a n a i r l i n e s) = 0.4765$

$r (w i t h H a w a i i a n a i r l i n e s) = 0.4838$

Part (c) Predicted $y$ with Hawaiian airlines is $34.1282$ and without Hawaiian airlines is $29.8402$

Part (a)

Step by step solution

Part (a) Step 1: Given information

Airline	Outsource percent	Delay Percent
AirTran	66	14
American	46	26
America west	76	39
ATA	18	19
Continental	69	20
Delta	48	26
Frontier	65	31
Hawaiian	80	70
Jet blue	68	18
Northwest	76	43
Southwest	68	20
United	63	27
US airways	77	24
Alaska	92	42

Part (a) Step 2: Concept

Linear regression is commonly used for predictive analysis and modeling.

Part (a) Step 3: Explanation

Place the explanatory variable (outsource percent) on the horizontal axis and the response variable (delay percent) on the vertical axis. Our completed scatterplot is shown below.

The residual plot for the regression is shown in the diagram below. Because it has the highest residual, a Hawaiian airline is an outlier.

Therefore, the required scatterplot is drawn.

Part (b) Step 1: Explanation

We may calculate the correlation r with Hawaiian Airlines as $r (w i t h H a w a i i a n A i r l i n e s) = 0.4765$ using a calculator.

Without Hawaiian Airlines, the correlation is $r (w i t h H a w a i i a n A i r l i n e s) = 0.4838 .$

Without Hawaiian Airlines, the correlation increases by $0.0073$ Taking Hawaiian Airlines out of the equation, on the other hand, has minimal effect on the association. Because of Hawaiian Airlines' exceptional position on the outsource percent scale, the position of the regression line is strongly influenced by this point. Therefore, correlation with Hawaiian airlines is $0.4765$ and correlation with Hawaiian airlines is $0.4838$

Part (c) Step 1: Calculation

The least-squares lines for forecasting $Y$ from $X$ with and without Hawaiian airlines are shown in the diagram below.

By deleting the point, Hawaiian Airlines is able to move the line quite a little. Because of Hawaiian Airlines' exceptional position on the outsourcing percent scale, the position of the regression line is strongly influenced by this point. Removing Hawaiian Airlines, on the other hand, has little effect on the regression line. We may acquire the linear equations of regression with and without Hawaiian airlines by utilizing a calculator.

Predicted $Y (w i t h H a w a i i a n a i r l i n e s) = 4.7314 + 0.3868 X$