Relationship between fuel use with weight of car and transmission type

1 Description of the data

The data is referred as mtcars in the R environment.

The data was extracted from the 1974 Motor Trend US magazine.

It contains performance for 32 automobiles (1973-74 models).

It also includes fuel consumption and 12 aspects of these models.

2 Summary statistics

2.1 Continuous variables

Summary statistics of continuous variables are presented in the following table.

	mpg	cyl	disp	hp	drat	wt	qsec
N	32.00	32.00	32.00	32.00	32.00	32.00	32.00
N_excl_NA	32.00	32.00	32.00	32.00	32.00	32.00	32.00
Min	10.40	4.00	71.10	52.00	2.76	1.51	14.50
Max	33.90	8.00	472.00	335.00	4.93	5.42	22.90
AM	20.09	6.19	230.72	146.69	3.60	3.22	17.85
GM	19.25	5.92	197.32	131.88	3.56	3.07	17.76
HM	18.44	5.65	166.80	118.23	3.52	2.92	17.68
Q1	15.43	4.00	120.83	96.50	3.08	2.58	16.89
Q2	19.20	6.00	196.30	123.00	3.70	3.33	17.71
Q3	22.80	8.00	326.00	180.00	3.92	3.61	18.90
Range	23.50	4.00	400.90	283.00	2.17	3.91	8.40
IQR	7.38	4.00	205.18	83.50	0.84	1.03	2.01
Var	36.32	3.19	15360.80	4700.87	0.29	0.96	3.19
SD	6.03	1.79	123.94	68.56	0.53	0.98	1.79
CV	0.30	0.29	0.54	0.47	0.15	0.30	0.10

2.2 Variable mpg & wt by am

Summary statistics of mpg and wt by am are presented in the following table.

am	mpg	wt
0	17.15	3.77
1	24.39	2.41

3 Summary plots

3.1 Pairwise plots

3.2 Scatter plot of mpg and wt

3.3 Boxplot of mpg with am

4 Linear Regression Model

• We modelled the fuel efficiency (mpg) to investigate the effect of:

  • weight of the car (wt) and

  • transmission type (am)

• We fitted a linear regression model with wt and am as predictors.

• The model also included the two-way interaction terms of wt and am.

4.1 Model in R

fm.lm <- lm(mpg ~ wt + am + wt:am, data=DF)

4.2 R Outputs

summary(fm.lm)

Call:
lm(formula = mpg ~ wt + am + wt:am, data = DF)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.6004 -1.5446 -0.5325  0.9012  6.0909 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  31.4161     3.0201  10.402 4.00e-11 ***
wt           -3.7859     0.7856  -4.819 4.55e-05 ***
am1          14.8784     4.2640   3.489  0.00162 ** 
wt:am1       -5.2984     1.4447  -3.667  0.00102 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.591 on 28 degrees of freedom
Multiple R-squared:  0.833, Adjusted R-squared:  0.8151 
F-statistic: 46.57 on 3 and 28 DF,  p-value: 5.209e-11

4.3 Summary

Estimates and standard errors of fitted linear regression model

Estimate	Std. Error	t value	Pr(>|t|)
31.416055	3.020109	10.402291	0.000000
-3.785908	0.785648	-4.818836	0.000046
14.878423	4.264042	3.489277	0.001621
-5.298360	1.444699	-3.667449	0.001017

4.4 Residual Plot

Model assumptions are checked by different plots of the residuals.

4.5 Conclusion

We observed that the two-way interaction effect of wt and am was significant.