Chapter 3.2, Problem 65E

(a)

To determine

To make: a scatterplot of the given data

Answer to Problem 65E

  

Explanation of Solution

Given:

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

Calculation:

Put outsource percent (the explanatory variable) on the horizontal axis and delay percent (the response variable) on the vertical axis. The below figure is our completed scatterplot.

  

The figure below shows residual plot for the regression. A Hawaiian airline is an outlier because it has largest residual.

  

Conclusion:

Therefore, the required scatterplot is drawn.

(b)

To determine

To find: the correlation r with and without Hawaiian Airlines.

Answer to Problem 65E

r (with Hawaiian airlines) = 0.4765

r (with Hawaiian airlines) = 0.4838

Explanation of Solution

Calculation:

By using calculator, we get correlation r with Hawaiian airlines is r (with Hawaiian airlines) = 0.4765

And correlation r without Hawaiian airlines is r (with Hawaiian airlines) = 0.4838

Correlation increases by 0.0073 without Hawaiian airlines. However, removing Hawaiian airlines has little effect on the correlation. Because of Hawaiian airline's extreme position on outsource percent scale; this point has a strong influence on the position of the regression line.

Conclusion:

Therefore, correlation with Hawaiian airlines is 0.4765 and correlation with Hawaiian airlines is 0.4838

(c)

To determine

To find: the least squares line

Answer to Problem 65E

Predicted $\widehat{Y}$

with Hawaiian airlines is 34.1282 and without Hawaiian airlines is 29.8402

Explanation of Solution

Calculation:

The below figure shows least squares lines for predicting Y from X with and without Hawaiian airlines.

  

You can see that removing the point Hawaiian airlines moves the line quite a bit. Because of Hawaiian airline's extreme position on outsource percent scale; this point has a strong influence on the position of the regression line. However, removing Hawaiian airlines has a little effect on the regression line. By using calculator, we get the linear equations of regression with and without Hawaiian airlines are,

Predicted $\widehat{Y}$ (with Hawaiian airlines) = $4.7314+0.3868X$

Predicted $\widehat{Y}$ (without Hawaiian airlines) = $10.8782+0.2495X$

Predicted percent of delays blamed on an airline that has outsourced 76% of its major maintenance is,

Predicted $\widehat{Y}$ (with Hawaiian airlines) $=4.7314+0.3868\times 76$

  $=34.1282$

Predicted $\widehat{Y}$ (without Hawaiian airlines) $=10.8782+0.2495X$

  $=10.8782+0.2495\times 76=29.8402$

Conclusion:

Therefore, predicted $\widehat{Y}$ with Hawaiian airlines is 34.1282 and without Hawaiian airlines is 29.8402