BBS300: Business Research Methodology Assignment on Fuel Consumption

This assignment analyzes fuel consumption in the car industry using a provided dataset and SPSS. The research explores the relationship between fuel consumption and engine horsepower using Pearson correlation, finding a strong positive correlation. It also investigates the impact of the number of cylinders on fuel consumption using one-way ANOVA, revealing significant differences between cylinder configurations. Finally, it employs regression analysis to predict fuel consumption based on car weight and acceleration time, with the model explaining a significant portion of the variance. The assignment adheres to specific assumptions for each statistical test, addressing normality, linearity, and equal variances, and provides detailed results and interpretations for each research question, including post-hoc analyses for ANOVA.

Business research Methodology
Student Name:
Instructor Name:
Course Number:
12th May 2019

Research question 1
Comparison of fuel consumption based on engines horse power
Technique to be used
We are going to use Pearson correlation test. This is based on the fact that we need to test for the
relationship between two continuous variables (fuel consumption and the engines horse power).
The test will reveal whether the two variables are correlated and we can also tell the direction
and strength of the relationship between these two variables using the proposed Pearson
correlation test (Nikolić, Muresan, Feng, & Singer, 2012).
Setting the hypothesis test
In this section, we sought to test whether the average fuel consumptions varies based on the car’s
engine horse power. The research question we sought to answer is whether there is significant
relationship between fuel consumption and the engines horse power. The following is the
hypothesis to be tested;
Null hypothesis (H0): There is no significant relationship between fuel consumption and the
engines horse power.
Alternative hypothesis (HA): There is significant relationship between fuel consumption and the
engines horse power.
This hypothesis was to be tested at 5% level of significance using Pearson correlation test.
Assumptions needed to use Pearson correlation
The following are the assumption needed to perform Pearson correlation test;

i) The levels of measurement of each variable should be continuous
ii) Absence of outliers in the dataset
iii) Normality of the variables. The variables need to follow a normal distribution.
iv) Linearity of the variables. The variables need to be linear
v) Related pair; each subject need to a pair of values.
Checking if the assumptions are met
i) The levels of measurements for both the two variables are continuous. This means
that the assumption on level of measurement is met for both the two variables.
ii) Linearity of variables. This assumption has been met since both the two variables are
linear.
iii) Related pair. The assumption on related pair was met since each subject had a pair of
values related to it.
iv) Test of normality
Results on normality test is presented below;
Table 1: Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
GallonsPer100Miles .114 392 .000 .943 392 .000
Hores Power of the
Engine
.164 392 .000 .904 392 .000
a. Lilliefors Significance Correction
From the results (considering either Shapiro-Wilk test or Kolmogorov-Smirnov test) it is
clear that both the two variables are not normally distributed (p < 0.05). This means that
the assumption on normality is violated.

v) Test for the presence of outliers

Considering the boxplots above, it is clear that the two variables have outliers. This
means that the assumption on outlier absence is violated.
Results
The results of the test are presented below;
Table 2: Correlations

GallonsPer100Mi
les
Horse Power of
the Engine
GallonsPer100Miles
Pearson Correlation 1 .854**
Sig. (2-tailed) .000
N 392 392
Horse Power of the Engine
Pearson Correlation .854** 1
Sig. (2-tailed) .000
N 392 392
**. Correlation is significant at the 0.01 level (2-tailed).
A Pearson correlation test was performed to assess the relationship between fuel consumption
(Gallons per 100 miles) and the horse power of the engine. There was a strong positive
correlation between the two variables, r = 0.854, n = 392, p = 0.000. A scatterplot below
summarizes the results. Overall, there was a strong, positive correlation between fuel
consumption (Gallons per 100 miles) and the horse power of the engine. Increases in the horse
power of the engine was correlated with increase in the fuel consumption (gallons per 100 miles).
Cars with lower engine horse power consumed less as compared to the cars with higher engine
horse power.

Research question 2:
Comparison of fuel consumption based on number of cylinders
Technique to be used
We are going to use one-way analysis of variance (ANOVA). This is based on the fact that we
need to test for the differences in the average fuel consumption among more than two different
factors (number of cylinders). The test will reveal whether the there is evidence of significant
difference in the fuel consumption for the five different cylinders (Spurrier, 2010).

Setting the hypothesis test
In this section, we sought to test whether the average fuel consumptions varies based on the car’s
number of cylinders. The research question we sought to answer is whether there is significant
differences in the average fuel consumption between the cylinders. The following is the
hypothesis to be tested;
Null hypothesis (H0): There is no significant difference in the average fuel consumption based on
the number of cylinders.
Alternative hypothesis (HA): At least one of the cylinders is different.
This hypothesis was to be tested at 5% level of significance using one-way analysis of variance
(ANOVA).
Assumptions needed to use Pearson correlation
The following are the assumption needed to perform Pearson correlation test;
i) Normality; the residual terms are assumed to follow a normal distribution
ii) Independence of the factors. The factors involved (number of cylinders) are assumed
to independent of each other.
iii) Assumption on equal variance. There is assumption that the variances for the factors
are equal. This is also known as homoscedasticity.
Checking if the assumptions are met
i) Test of normality
Results on normality test is presented below;
Table 3: Tests of Normality

Number of
cylinders
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Gallons Per
100Miles
3 .212 4 . .964 4 .804
4 .077 199 .006 .980 199 .007
5 .191 3 . .997 3 .900
6 .094 83 .064 .966 83 .028
8 .131 103 .000 .969 103 .016
a. Lilliefors Significance Correction
As can be seen in the above table (table 3), we can see that the assumption of
normality is violated for some cylinders (p < 0.05).
ii) Test of equal variances
Results of the test of homogeneity of variances (equal variances)
Table 4: Test of Homogeneity of Variances
Gallons Per 100Miles
Levene Statistic df1 df2 Sig.
7.508 4 387 .000
As can be seen in the above table (table 3), we can see that the assumption of equal
variances is violated (p < 0.05).
iii) Independence of factors. The factors were however found to be independent hence
the assumption of independence was met.
Results
The results on research question 2 are presented below;
Table 5: Descriptive (summary) statistics
Gallons Per 100Miles
N Mean Std.
Deviation
Std. Error 95% Confidence Interval for
Mean
Minimum Maximum

Lower Bound Upper Bound
3 4 4.9500 .62450 .31225 3.9563 5.9437 4.20 5.60
4 199 3.5362 .68016 .04822 3.4411 3.6313 2.10 5.60
5 3 3.8333 1.10151 .63596 1.0970 6.5696 2.70 4.90
6 83 5.1711 .80993 .08890 4.9942 5.3479 2.60 6.70
8 103 6.9068 1.21448 .11967 6.6694 7.1442 3.80 11.10
Total 392 4.7847 1.66864 .08428 4.6190 4.9504 2.10 11.10
From the summary table above (table 5), we can see that cars with 8 cylinders consume more
than all the other cars (M = 6.91, SD = 1.21, N = 103). Cars with 6 cylinders consume an average
of 5.17 (SD = .81, N = 83), those with 5 cylinders consume an average of 3.83 (SD = 1.10, N =
3). Results further revealed that cars with 4 cylinders consumed the least fuel (M = 3.54, SD
= .68, N = 199) while cars with 3 cylinders consumed an average of 4.95 (SD = .62, N = 4).
Table 6: ANOVA
Gallons Per 100Miles
Sum of Squares df Mean Square F Sig.
Between Groups 789.256 4 197.314 255.018 .000
Within Groups 299.432 387 .774
Total 1088.688 391
Table 6 above presents the ANOVA results. As can be seen, there is sufficient evidence to reject
the null hypothesis and conclude that at least on the cylinders is different (p < 0.05).
Table 7: Multiple Comparisons
Dependent Variable: Gallons Per 100Miles
LSD
(I) Number
of cylinders
(J) Number
of cylinders
Mean Difference
(I-J)
Std. Error Sig. 95% Confidence Interval
Lower Bound Upper Bound
3
4 1.41382* .44421 .002 .5405 2.2872
5 1.11667 .67182 .097 -.2042 2.4375
6 -.22108 .45028 .624 -1.1064 .6642
8 -1.95680* .44827 .000 -2.8381 -1.0755
4 3 -1.41382* .44421 .002 -2.2872 -.5405

5 -.29715 .51166 .562 -1.3031 .7088
6 -1.63490* .11494 .000 -1.8609 -1.4089
8 -3.37062* .10677 .000 -3.5805 -3.1607
5
3 -1.11667 .67182 .097 -2.4375 .2042
4 .29715 .51166 .562 -.7088 1.3031
6 -1.33775* .51694 .010 -2.3541 -.3214
8 -3.07346* .51519 .000 -4.0864 -2.0605
6
3 .22108 .45028 .624 -.6642 1.1064
4 1.63490* .11494 .000 1.4089 1.8609
5 1.33775* .51694 .010 .3214 2.3541
8 -1.73571* .12975 .000 -1.9908 -1.4806
8
3 1.95680* .44827 .000 1.0755 2.8381
4 3.37062* .10677 .000 3.1607 3.5805
5 3.07346* .51519 .000 2.0605 4.0864
6 1.73571* .12975 .000 1.4806 1.9908
*. The mean difference is significant at the 0.05 level.
Post hoc analysis test further revealed that significant differences were observed between
cylinder 3 (M = 4.95, SD = .62, N = 4) and cylinder 4 (M = 3.54, SD = .68, N = 199), between
cylinder 3 (M = 4.95, SD = .62, N = 4) and cylinder 8 (M = 6.91, SD = 1.21, N = 103), between
cylinder 4 (M = 3.54, SD = .68, N = 199) and cylinder 6 (M = 5.17, SD = .81, N = 83), between
cylinder 4 (M = 3.54, SD = .68, N = 199) and cylinder 8 (M = 6.91, SD = 1.21, N = 103).
However, there were no significant differences in the average fuel consumption between cylinder
3 (M = 4.95, SD = .62, N = 4) and cylinder 5 (M = 3.83, SD = 1.10, N = 3) and also between
cylinder 4 4 (M = 3.54, SD = .68, N = 199) and cylinder 5 (M = 3.83, SD = 1.10, N = 3).

Research question 3
Predicting fuel consumption
Technique to be used