Answer To: Criteria Excellent Good Satisfactory Not Satisfactory Poor Introduction and Parameter Justification...
Pooja answered on May 05 2021
Table of Contents
Introduction 2
Parameters and the sample population 3
Collected data 3
Descriptive statistics 5
Regression Analysis 10
Model 10
Coefficient of the independent variables 11
Assumptions of regression analysis 13
Multi-co-linearity 14
Normality of Residuals 15
Homogeneity of Residuals 15
Conclusion 18
Further Research 19
References 20
Introduction
I want to analyse if Fuel Load can be predicted with the help of Fuel Mass, Cell Lower Area, Height, and Total Pressure 3.75 G. The dependent variable is Fuel Load. The independent variables are Fuel Mass, Cell Lower Area, Height, and Total Pressure 3.75 G. Descriptive analysis is used to understand the variables involved in data. The technique of regression analysis is used to build an appropriate regression model. The assumptions of regression analysis are also checked.
Parameters and the sample population
The population consists of all type of airplanes. The sample consists of randomly selected 39 airplanes.
Collected data
The dataset of applied fuel pressures is obtained from a secondary source. The source of data is Coordinating Research Council, Inc., Handbook of Aviation Fuel Properties, Society of Automotive Engineers, Inc., CRC Report No. 530, Warrendale, PA, 1983.
All the variables namely fuel load, fuel mass, sugar area, height, and total pressure 3.75 G are continuous variables. All these variables are measured by the ratio scale of measurement. The measure of fuel mass in kilograms. The measure of cell lower area and height is meter square and meters respectively. The Total pressure 3.75 G is measured in N/m^2. Wilcox, R. R. (1996).
There is a total of 39 observations in this data which corresponds to volume ID. Volume ID is the same as bay number, i.e., volume 1 is contained by ribs 1 & 2. The data is shown below.
Fuel Load (N)
Fuel Mass (kg)
Cell Lower Area (m^2)
Height (m)
Total Pressure 3.75 G (N/m^2)
35317.37007
3595.7412
3.881
0.9146
34125.26095
36854.96488
3752.2872
3.881
0.9146
35610.9555
35017.73621
3565.2348
3.881
0.9146
33835.74099
5647.309766
574.96536
0.6002
1.12
35283.92473
17189.52149
1750.104
1.799
1.147
35831.40944
27172.06011
2766.4488
2.997917662
1.145
33988.66711
23552.79848
2397.9636
2.829076
0.9146
31219.73192
20856.09373
2123.406
2.612
0.8015
29942.70731
19846.80073
2020.6476
2.55
0.7814
29186.47166
13202.81412
1920.2976
2.488
0.7612
28428.1999
12529.42644
1822.356
2.426
0.7411
27667.73593
15327.849
2229.3756
3.065
0.7209
26790.69389
20359.33233
2072.8296
2.96
0.6947
25793.07305
13586.03006
1383.2244
2.043
0.6684
24937.64695
12821.1752
1305.3528
1.984
0.6498
24233.57208
12150.94157
1237.1148
1.937
0.6312
23524.02213
11464.93773
1167.2712
1.883
0.6125
22832.45697
10771.04879
1096.6248
1.825
0.5938
22132.29203
10156.01086
1034.0064
1.777
0.5752
21432.212
9501.547428
967.374
1.719
0.5566
20727.63401
8918.04991
907.9668
1.671
0.5379
20013.577
8334.552391
848.5596
1.618
0.5193
19316.79324
7741.592751
788.18904
1.56
0.5006
18609.59796
7216.444984
734.72256
1.512
0.482
17897.92903
6670.007443
679.08852
1.454
0.4633
17202.5639
6181.919654
629.3952
1.406
0.4447
16488.05029
5694.620376
579.78216
1.352
0.426
15794.98995
5211.263647
530.57052
1.296
0.4074
15078.88787
4779.16008
486.57708
1.246
0.3888
14383.50746
4339.17141
441.78084
1.19
0.3701
13673.85949
3944.12782
401.56056
1.14
0.3515
12974.10467
1747.338515
177.90048
0.5263
0.3328
12450.16042
1670.853029
170.11332
0.5173
0.3239
12112.31173
3404.786871
346.64904
1.104
0.3149
11565.1728
3016.051362
307.071
1.046
0.295
10812.80364
2635.200955
268.29576
0.9823
0.275
10060.06676
2288.256484
232.97256
0.9218
0.2551
9308.919306
1969.69838
200.53944
0.8636
0.2352
8552.997827
1665.333458
169.55136
0.8006
0.2152
7800.400284
Descriptive statistics
The table of descriptive statistics for Fuel Load (N) along with corresponding histogram is given below.
Fuel Load (N)
Mean
11557.79996
Standard Error
1535.795776
Median
8918.04991
Mode
#N/A
Standard Deviation
9591.04155
Sample Variance
91988078.01
Kurtosis
1.138028335
Skewness
1.309505799
Range
35189.63142
Minimum
1665.333458
Maximum
36854.96488
Sum
450754.1985
Count
39
The distribution of fuel load is positively skewed. This implies there are very few aircraft with high fuel load. This is evident from the histogram as it has a tail towards the right.
The average fuel load is 11558 with a high standard deviation of 9591. The higher standard deviation indicates that mean is not considered as the best measure of Central Tendency. For a skewed distribution, the median is considered as a reliable measure of Central Tendency. The median through fuel load is 8918. Wilcox, R. R. (1996).
The descriptive statistics and the corresponding histogram for fuel mass are given below.
Fuel Mass (kg)
Mean
1222.664
Standard Error
160.2214
Median
907.9668
Mode
#N/A
Standard Deviation
1000.582
Sample Variance
1001165
Kurtosis
0.538329
Skewness
1.121282
Range
3582.736
Minimum
169.5514
Maximum
3752.287
Sum
47683.91
Count
39
The distribution of fuel mass is approximately normally distributed. The average fuel mass is 1223 Kg with a low standard deviation of 160 units. The minimum and maximum fuel mass is 170 kg and 3752 kg. Huck, S. W., Cormier, W. H., & Bounds, W. G. (1974).
The descriptive statistics and the corresponding histogram for Cell Lower Area are given below.
Cell Lower Area (m^2)
1222.664
Mean
160.2214
Standard Error
907.9668
Median
#N/A
Mode
1000.582
Standard Deviation
1001165
Sample Variance
0.538329
Kurtosis
1.121282
Skewness
3582.736
Range
169.5514
Minimum
3752.287
Maximum
47683.91
Sum
39
Count
The distribution of cell lower area is approximately normally distributed. This is evident from the bell-shaped histogram. The average cell lower area is 1.8 meter square with a noticeable standard deviation of 0.9 units. The minimum and maximum cell lower area is 0.5-meter square and 3.9-meter square. Fisz, M., & Bartoszyński, R. (2018).
The descriptive statistics and the corresponding histogram for Height of Airplanes are given below.
Height (m)
Mean
0.589677
Standard Error
0.041427
Median
0.5566
Mode
0.9146
Standard Deviation
0.258712
Sample Variance
0.066932
Kurtosis
-0.42617
Skewness
0.580016
Range
0.9318
Minimum
0.2152
Maximum
1.147
Sum
22.9974
Count
39
The distribution of height of the airplanes is approximately normally distributed. This implies that empirical rule can be applied here. The height of the airplane has an average of 0.6 meters with a standard deviation of 0.3. The minimum and maximum value corresponding to the height of the airplane is 0.2 and 1.14. Fisz, M., & Bartoszyński, R. (2018).
The descriptive statistics and the corresponding histogram for Total Pressure 3.75 G of Airplanes are given below.
Total Pressure 3.75 G (N/m^2)
Mean
21323.62
Standard Error
1372.637
Median
20727.63
Mode
#N/A
Standard Deviation
8572.116
Sample Variance
73481166
Kurtosis
-1.13194
Skewness
0.198494
Range
28031.01
Minimum
7800.4
Maximum
35831.41
Sum
831621.1
Count
39
The distribution of Total Pressure 3.75 G of the airplanes is approximately normally distributed. This implies that empirical rule can be applied here. The Total Pressure 3.75 G of the airplane has an average of 21323.62 N/m^2 with a standard deviation of 8572. The minimum and maximum value corresponding to the Total Pressure 3.75 G of the airplane is 7800 and 35831. Fisz, M., & Bartoszyński, R. (2018).
Regression Analysis
Model
The regression output as obtained from the Excel is given below.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.988031
R Square
0.976206
Adjusted R Square
0.973407
Standard Error
1564.05
Observations
39
ANOVA
df
SS
MS
F
Significance F
Regression
4
3.41E+09
8.53E+08
348.7347
4.42E-27
Residual
34
83172635
2446254
Total
38
3.5E+09
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
2546.853
1655.837
1.538106
0.133278
-818.212
5911.919
Fuel Mass (kg)
11.94972
1.641744
7.278672
1.99E-08
8.613293
15.28614
Cell Lower Area (m^2)
-2161.08
1612.513
-1.3402
0.18907
-5438.1
1115.938
Height (m)
2961.189
6663.565
0.444385
0.65958
-10580.8
16503.18
Total Pressure 3.75 G (N/m^2)
-0.15909
0.224653
-0.70814
0.483684
-0.61564
0.297463
The regression equation is given by: Fuel Load (N) = 2546.853 + 11.94972*Fuel...