# Analyzing the Impact of Pilot Age on Aviation Events: Regression Modeling Insights

June 07, 2023
Emily Cooper
🇺🇸 United States
Statistics
Emily Cooper is a seasoned statistician with a decade of experience and a Ph.D. from the University of Pennsylvania. Specializing in assisting students with their assignments, she offers expertise in all areas of statistics.
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Key Topics
• Problem Description:
• Part 1 – Linear vs. Quadratic Models
• Import Data:
• Linear Regression Analysis:
• Model Selection:
• Practical Implications:
• Part 2 – Linear vs. Logarithmic Models
• Import Data:
• Linear Regression Analysis:
• Model Selection:
• Practical Implications:

## Problem Description:

This regression analysis assignment delves into the complex relationship between pilot age and aviation events, examining two distinct datasets: Parabolic Data and Logarithmic Data. The "number of events per age" is the focal point in the Parabolic Data, while the Logarithmic Data centers on the "event rate per 1000 hours." The task at hand is to employ rigorous statistical methods to uncover the most suitable regression models that can shed light on the impact of pilot age on aviation events and, ultimately, to provide a comprehensive interpretation of the results.

### Import Data:

First, we meticulously import data from the Excel file labeled "Parabolic Data" into SPSS, ensuring data integrity and precision.

la Even!IDYNumberofEven tsperAgeXPilotAge
120041020X016591729
220090213X136132147
320001212X223141836
420041020X016592548
520060828X012443044
620001212)(223143044
720060131X001402041
820001212)(203392453
920060131X001402354
1020010214X004493044
1120001211X108321327
1220001212)(206241626
1320010214X004491729
1420001211X094941327
1520010112X002921238
1620010112X002923044
1720030605X008002235
1820070409X003872637
Ans: Data imported in SPSS 27

### Linear Regression Analysis:

Model Summary
ModelRR SquareAdjusted R SquareStd. Error of the Estimate
1.350a.122.1205.826
a. Predictors: (Constant), X = Pilot Age
ANOVAa
ModelSum of SquaresdfMean SquareFSig.
1Regression1411.99811411.99841.598.000b
Residual10115.28229833.944
Total11527.280299
a. Dependent Variable: Y = Number of Events per Age
b. Predictors: (Constant), X = Pilot Age
Coefficientsa
ModelUnstandardized CoefficientsStandardized CoefficientstSig.
BStd. ErrorBeta
1(Constant)11.9191.4967.967.000
X = Pilot Age.226.035.3506.450.000
a. Dependent Variable: Y = Number of Events per Age
• A meticulous linear regression analysis is executed to create a model that dissects the relationship between pilot age and the number of events per age.

Results and Interpretation:

• The R-squared (R2) value stands at 0.122, indicating that approximately 12.2% of the variance in the number of events per age can be attributed to pilot age.

Regression Equation:

• The resulting regression equation is expressed as No. of events per age = 11.919 + 0.226 × Age.
• The interpretation reveals that for every one-year increase in pilot age, the number of events per age experiences an average rise of 0.226.

Scatter Plot Analysis:

scatter plot between Y and X.

• A visual analysis of the scatter plot unveils a parabolic relationship, where the number of events initially surges with age, peaks around 45 years, and subsequently begins to decline.

• Given the inherent nonlinearity in the data, a quadratic model is employed, delivering a far superior fit.

R2 for the quadratic model is calculated at 0.581.

### Model Selection:

• The assignment recommends reporting the quadratic model due to its superior fit, offering a more comprehensive explanation of the data than the linear model.

### Practical Implications:

• Beyond the statistical analysis, this study carries practical implications, such as identifying age-related trends, devising risk models for predictions, and facilitating targeted interventions based on age-related risk factors.

## Part 2 – Linear vs. Logarithmic Models

### Import Data:

• Just as in Part 1, we import the dataset from the Excel file labeled "Logarithmic Data" into SPSS.

£ EventlDXPilotAgeYEventRateper1000ho urs
120041020X0165929.307848321321213
220090213X1361347.097783117046392
320001212X2231436.199423886549967
420041020X0165948.097470826981485
520060828X0124444.118730063243547
620001212X2231444.118730063243547
720060131X0014041.144561941177746
820001212X2033953.091108563445726
920060131X0014054.089624589870084
1020010214X0044944.118730063243547
1120001211X1083227.405098002555234
1220001212X2062426.532197977647685
1320010214X0044929.307848321321213
1420001211X0949427.405098002555234
1520010112)(0029238.211718625946118
1620010112)(0029244.118730063243547
1720030605X0080035.178848702127490
Ans: Imported data into SPSS 27

### Linear Regression Analysis:

Model Summary
ModelRR SquareAdjusted R SquareStd. Error of the Estimate
1.847a.718.717.065660494985265
a. Predictors: (Constant), X = Pilot Age
ANOVAa
ModelSum of SquaresdfMean SquareFSig.
1Regression3.27213.272758.915.000b
Residual1.285298.004
Total4.557299
a. Dependent Variable: Y = Event Rate per 1000 hours
b. Predictors: (Constant), X = Pilot Age
Coefficientsa
ModelUnstandardized CoefficientsStandardized CoefficientstSig.
BStd. ErrorBeta
1(Constant).638.01737.820.000
X = Pilot Age-.011.000-.847-27.548.000
a. Dependent Variable: Y = Event Rate per 1000 hours
• A meticulous linear regression analysis is undertaken to untangle the intricate relationship between pilot age and the event rate per 1000 hours.
• Results and Interpretation:
• The linear model yields an R2 value of 0.718, signifying that approximately 71.8% of the variance in the event rate per 1000 hours can be attributed to pilot age.
• Regression Equation:
• The linear regression equation materializes as Event rate per 1000 hours = 0.638 - 0.011 × Age.
• Interpretation reveals that with each one-year increase in age, there is a decrease of 0.011 in the event rate per 1000 hours.

•Scatter Plot Analysis:

The relationship portrayed in the scatter plot is intricate and nonlinear, resembling a hyperbola. The event rate sharply declines with age, more significantly in younger pilots.

• Curve Estimation - Logarithmic Model:
• To enhance the accuracy of the model, we employ a logarithmic model. This choice leads to a superior fit, with an R2 of 0.799.

### Model Selection:

In line with Part 1, the assignment advocates for reporting the logarithmic model, which offers a superior fit across pilots of all ages compared to the linear model.

### Practical Implications:

The results of this study have broader applications, aiding in identifying age-related patterns, developing accurate risk models, and influencing training, selection, and policy decisions within the aviation industry.

In summary, this assignment underscores the significance of employing sophisticated regression models, particularly the quadratic and logarithmic models, to discern the multifaceted interplay between pilot age and aviation events. Such insights have far-reaching applications, shaping the future of aviation practice and policy.

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