Regression Analysis of Fuel Prices

This document discusses the regression analysis of fuel prices in different locations. It includes scatter plots, regression equations, correlation coefficients, and coefficients of determination. The document also compares simple linear regression models with multiple linear regression models.

Question 1 Statistical Inference
Regression analysis was utilised to observe the behaviour of the fuel prices in different locations.
Excel was used to obtain the results as well as the graphs. The obtained results are attached in the
appendices. The graph obtained from the analysis is shown in figure 1.
0 20 40 60 80 100 120
115
120
125
130
135
140
145
150
155
160
Normal Probability Plot
Sample Percentile
147
Figure 1: Normal probability plot for the unleaded 91
From the graph we can compare the prices of fuel in the different locations and how they deviate
from the mean. The scatter plot shows that the deviation from the mean is evenly distributed
across the percentiles (Montgomery, 2012). The data in excel obtained the residual values in
each region. The values show that the prices greatly deviated from the mean (check appendices 1
and excel). The R square value is 0.5324 which indicates that the data is far off from the fitted
regression line (Seber, 2012).

Question 2 Simple linear regression model
The scatter plot is shown in figure 2.
0 20 40 60 80 100 120
115
120
125
130
135
140
145
150
155
160
Normal Probability plot
Percentile
Fuel prices
Figure 2: Normal probability plot for unleaded 91 and diesel prices
The least square regression equation was also solved using excel as shown.

0 20 40 60 80 100 120
115
120
125
130
135
140
145
150
155
160
f(x) = 0.307513461538462 x + 128.088883885102
R² = 0.985094971839995
Normal Probability plot
Percentile
Fuel prices
Figure 3: Scatter plot and linear trendline of the fuel prices
The equation is y=0.3075 x +128.09
Correlation coefficient and coefficient of determination were calculated in excel and the value
obtained as
Multiple R = 0.67804985
R2=0.4597516
The gradient of curve represents the average change in fuel price between two regions (Cameron,
2013).
The intercept is the lowest possible fuel price in the country.
Correlation coefficient showed the relationship between the unleaded 91 and diesel prices (Peng,
2015).
Coefficient of determination showed the proportion of the variance in the unleaded 91 and diesel
price that is predictable from the location (Bolin, 2013).
Question 3 Multiple Regression Model
The graphs are shown

0 20 40 60 80 100 120
115
120
125
130
135
140
145
150
155
160 Normal Probability Plot
Sample Percentile
147
135.0 140.0 145.0 150.0 155.0 160.0 165.0
0.0
20.0
40.0
60.0
80.0
100.0
120.0
140.0
160.0
180.0
f(x) = 1.09452616101194 x − 21.6869714492974
R² = 1
148 Line Fit Plot
148
147
From excel file, we obtained:

Multiple regression equation y=1.0945 x−21.687
Multiple correlation factor R = 0.67805
Coefficient of multiple determination R2=0.45975
Multiple correlation coefficient showed the relationship between the unleaded 91 and diesel
prices in relation to the location (Chatterjee, 2015).
Coefficient of multiple determination showed the proportion of the variance in the unleaded 91
and diesel price factoring in the location that can be predicted.
The values of coefficients for the simple linear regression model were similar to the multiple
linear regression model.
Multiple linear regression model was more detailed than the linear regression model. This made
it more appropriate in predicting the price of dependent fuel.

Appendices 1
SUMMAR
Y OUTPUT
Regression
Statistics
Multiple R
0.72962817
8
R Square
0.53235727
8
Adjusted R
Square
0.52628399
6
Standard
Error
6.19476639
9
Observation
s 79
ANOVA
df SS MS F
Significanc
e F
Regression 1
3363.79
6
3363.79
6 87.65562
2.40533E-
14
Residual 77
2954.88
5
38.3751
3
Total 78
6318.68
1
Coefficient
s
Standar
d Error t Stat P-value Lower 95%
Upper
95%
Lower
95.0%
Upper
95.0%
Intercept
155.196864
7
1.43390
3
108.233
9 6.81E-86
152.341599
2
158.052
1
152.341
6
158.052
1
1
-
0.28615384
6
0.03056
4
-
9.36246 2.41E-14
-
0.34701447
9
-
0.22529 -0.34701 -0.22529
RESIDUAL
OUTPUT
PROBABILIT
Y OUTPUT
Observatio
n
Predicted
147
Residua
ls Percentile 147
1 154.624557
1.27544
3 0.632911 130.5

2
154.338403
1
1.56159
7 1.898734 130.7
3
154.052249
3
1.84775
1 3.164557 130.7
4
153.766095
4
1.13390
5 4.43038 130.7
5
153.479941
6
2.42005
8 5.696203 130.7
6
153.193787
7
0.70621
2 6.962025 130.9
7
152.907633
9
0.99236
6 8.227848 130.9
8 152.62148 1.37852 9.493671 130.9
9
152.335326
2
-
4.43533 10.75949 130.9
10
152.049172
3
-
0.54917 12.02532 130.9
11
151.763018
5
2.13698
1 13.29114 130.9
12
151.476864
7
-
0.57686 14.55696 131.9
13
151.190710
8
4.70928
9 15.82278 132.2
14 150.904557
4.49544
3 17.08861 132.2
15
150.618403
1 -1.7184 18.35443 132.7
16
150.332249
3
2.56775
1 19.62025 132.9
17
150.046095
4 -8.1461 20.88608 134.9
18
149.759941
6
-
11.8599 22.1519 134.9
19
149.473787
7
5.42621
2 23.41772 134.9
20
149.187633
9
-
1.28763 24.68354 134.9
21 148.90148
-
3.00148 25.94937 135.4
22
148.615326
2
1.28467
4 27.21519 135.9
23
148.329172
3
7.57082
8 28.48101 135.9
24
148.043018
5
0.85698
1 29.74684 135.9
25 147.756864 8.14313 31.01266 136.9

7 5
26
147.470710
8
6.42928
9 32.27848 136.9
27 147.184557
-
2.28456 33.5443 137.4
28
146.898403
1
3.00159
7 34.81013 137.9
29
146.612249
3
-
14.4122 36.07595 138.4
30
146.326095
4
-
15.4261 37.34177 138.5
31
146.039941
6
-
0.13994 38.60759 138.9
32
145.753787
7
3.94621
2 39.87342 138.9
33
145.467633
9
3.53236
6 41.13924 139.9
34 145.18148 4.71852 42.40506 139.9
35
144.895326
2
2.00467
4 43.67089 139.9
36
144.609172
3
11.8908
3 44.93671 140.9
37
144.323018
5
0.37698
1 46.20253 141.9
38
144.036864
7
8.86313
5 47.46835 142.7
39
143.750710
8
12.1492
9 48.73418 143.4
40 143.464557
0.43544
3 50 143.9
41
143.178403
1
6.72159
7 51.26582 144.7
42
142.892249
3
-
6.99225 52.53165 144.9
43
142.606095
4
6.79390
5 53.79747 145.9
44
142.319941
6
-
2.41994 55.06329 145.9
45
142.033787
7
-
6.13379 56.32911 146.9
46
141.747633
9
-
5.84763 57.59494 147.9
47 141.46148
-
9.26148 58.86076 147.9
48
141.175326
2
-
6.27533 60.12658 147.9

49
140.889172
3
-
8.98917 61.39241 148.9
50
140.603018
5
7.29698
1 62.65823 148.9
51
140.316864
7
-
9.81686 63.92405 149
52
140.030710
8
-
9.33071 65.18987 149.4
53 139.744557
-
8.84456 66.4557 149.7
54
139.458403
1 -8.7584 67.72152 149.9
55
139.172249
3
-
8.47225 68.98734 149.9
56
138.886095
4 -5.9861 70.25316 149.9
57
138.599941
6
-
5.89994 71.51899 149.9
58
138.313787
7
2.58621
2 72.78481 149.9
59
138.027633
9
-
3.12763 74.05063 150.9
60 137.74148 0.75852 75.31646 151.5
61
137.455326
2
1.44467
4 76.58228 152.9
62
137.169172
3
5.53082
8 77.8481 152.9
63
136.883018
5
-
1.98302 79.11392 153.9
64
136.596864
7
-
1.19686 80.37975 153.9
65
136.310710
8
-
5.61071 81.64557 153.9
66 136.024557
7.37544
3 82.91139 153.9
67
135.738403
1 -0.8384 84.17722 154
68
135.452249
3
1.94775
1 85.44304 154.9
69
135.166095
4 -4.2661 86.70886 154.9
70
134.879941
6
3.52005
8 87.97468 155.4
71
134.593787
7
-
3.69379 89.24051 155.9
72 134.307633 15.5923 90.50633 155.9

9 7
73 134.02148 2.87852 91.77215 155.9
74
133.735326
2
-
2.83533 93.03797 155.9
75
133.449172
3
6.45082
8 94.3038 155.9
76
133.163018
5
3.73698
1 95.56962 155.9
77
132.876864
7
-
1.97686 96.83544 155.9
78
132.590710
8
7.30928
9 98.10127 155.9
79 132.304557
6.59544
3 99.36709 156.5

References
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Analysis: A Regression Based Approach. New York, NY: The Guilford Press.‐ Journal of Educational
Measurement, 51(3), pp.335-337.
Cameron, A.C. and Trivedi, P.K., 2013. Regression analysis of count data (Vol. 53). Cambridge university
press, pp. 12-17.
Chatterjee, S. and Hadi, A.S., 2015. Regression analysis by example. John Wiley & Sons, pp.
132-144.
Montgomery, D.C., Peck, E.A. and Vining, G.G., 2012. Introduction to linear regression analysis (Vol. 821).
John Wiley & Sons, pp. 22-76.
Peng, Mandal, J.K., Satapathy, S.C., Sanyal, M.K., Sarkar, P.P. and Mukhopadhyay, A. eds., 2015.
Information Systems Design and Intelligent Applications: Proceedings of Second International Conference
INDIA 2015 (Vol. 2). Springer, pp. 161-171.
Seber, G.A. and Lee, A.J., 2012. Linear regression analysis (Vol. 329). John Wiley & Sons, pp. 132-146.