Question

The remaining questions in this workbook assignment are based on the following scenario.

Information was collected from a reputable internet site for an investigation into the fuel economy of various makes of car and whether these varied over time. Data was collected for fifteen different models of vehicle from twelve different manufacturers. After collection, the observed vehicle models were classified as sedan, sports or 4WD.
The data for sedans is provided in the file sedan_economy.csv, also available in the same folder as this assignment. The variables in this file are:
decade: the decade in which the car was produced ((1991-2000, 2001-2010, 2011-present);
economy: fuel economy (L/100km);
cylinders: the number of cylinders in the engine;
capacity: the engine capacity (L);
fuel: the fuel type (petrol or diesel);
transmission: the transmission of the car (manual or automatic).

	decade	economy	cylinders	capacity	fuel	transmission
1	1991-2000	7.2	4	1.3	petrol	manual
2	2001-2010	6.8	4	1.6	petrol	manual
3	2011+	5.7	4	1.5	petrol	manual
4	2011+	4.9	3	1.0	petrol	manual
5	1991-2000	7.2	4	1.8	petrol	manual
6	2001-2010	7.5	4	2.0	petrol	manual
7	2001-2010	8.4	4	2.0	petrol	automatic
8	2011+	6.4	4	2.0	petrol	manual
9	2011+	6.1	4	2.0	petrol	automatic
10	1991-2000	7.1	4	1.8	petrol	manual
11	1991-2000	7.6	4	1.8	petrol	automatic
12	2001-2010	7.1	4	1.8	petrol	manual
13	2001-2010	7.5	4	1.8	petrol	automatic
14	2011+	7.2	4	1.8	petrol	manual
15	2011+	6.7	4	1.8	petrol	automatic
16	1991-2000	7.2	6	2.8	petrol	manual
17	2001-2010	7.7	4	2.0	petrol	manual
18	2001-2010	7.4	4	2.0	petrol	automatic
19	2011+	6.4	4	2.0	petrol	manual
20	2011+	6.8	4	2.0	petrol	automatic
21	2011+	3.6	4	1.6	diesel	manual
22	1991-2000	6.0	4	1.5	petrol	manual
23	1991-2000	6.1	4	1.5	petrol	automatic
24	2001-2010	7.3	4	1.6	petrol	manual
25	2001-2010	7.5	4	1.6	petrol	automatic
26	2001-2010	4.7	4	2.0	diesel	manual
27	2011+	6.7	4	1.6	petrol	manual
28	2011+	7.0	4	1.6	petrol	automatic
29	2011+	4.3	4	1.8	diesel	manual
30	1991-2000	9.2	6	4.0	petrol	manual
31	2001-2010	10.8	6	4.0	petrol	manual
32	2001-2010	10.3	6	4.0	petrol	automatic
33	2011+	11.3	6	4.0	petrol	manual
34	2011+	10.1	6	4.0	petrol	automatic
35	1991-2000	9.2	6	3.0	petrol	manual
36	1991-2000	9.0	6	3.0	petrol	automatic
37	2001-2010	11.7	6	3.5	petrol	manual
38	2011+	10.3	6	3.7	petrol	manual
39	2011+	10.4	6	3.7	petrol	automatic
40	1991-2000	10.5	8	5.0	petrol	manual
41	1991-2000	11.3	8	5.0	petrol	automatic
42	2001-2010	14.3	8	6.0	petrol	manual
43	2001-2010	14.2	8	6.0	petrol	automatic
44	2011+	11.6	8	6.0	petrol	manual
45	2011+	11.7	8	6.0	petrol	automatic
46	1991-2000	9.8	8	5.5	petrol	automatic
47	2001-2010	14.1	8	6.2	petrol	automatic
48	2011+	9.8	8	5.5	petrol	automatic

The sample averages of fuel economy for manual and automatic sedans in this sample are 7.854 L/100km and 9.09 L/100km, respectively. Based on this, one of the investigators has suggested that it may be possible to predict the transmission type of a sedan from its fuel economy, using a formal statistical analysis.
(a) Using R, create a new variable isauto that takes the value 1 if the transmission type is automatic, or a 0 if the transmission type is manual. You should show the command you used to do this.
(b) You should then fit an appropriate statistical model that describes the probability of a randomly chosen car having an utomatic transmission, where the fuel economy is a predictor. You should ensure you show the command you used to do this, and provide the coefficient/summary table.
(c) Is fuel economy a significant predictor of the probability of a randomly chosen car having an automatic transmission?
(d) Your friend is looking to purchase a sedan with a manual transmission from an online seller, who has not included the transmission type of the car in the advertisement description. However, the seller has stated in the advert that his 60L tank gives a range of 730km. Whether or not you found fuel economy to be a significant predictor in (d), calculate the average fuel economy and hence determine the model estimate of the probability of the car having a manual transmission.

Answer 1

Input:

dat<-read.csv("sedan_economy.csv",sep=",")
lookup<-c("automatic"=1,"manual"=0)
dat$new_transmission<-lookup[data$transmission]
dat
model<-lm(new_transmission~economy,data = dat)
summary(mod)
econ=data.frame(
economy=c(730/60)
)
predict(model,newdata=econ)

OUTPUT:

a)

We inserted the data into R using the read.csv function.

Next, we created a new variable lookup where "automatic"=1, "manual"=0

We inserted a new column in the data frame using

dat$new_transmission<-lookup[data$transmission]

b)

We fitted a model for new_transmission with the economy as a predictor

model<-lm(new_transmission~economy,data = dat)

c)

summary function gave us a summary of the model.

P-value > 0.05 so the model is significant,but Adjusted R-squared =0.038

i.e. only 3.8% of the variance in the predicted variable is defined by the model.

d)

We created a data frame having the fuel economy of the car we want to predict transmission of.

> econ=data.frame(
+ economy=c(730/60)
+ )

Next, we predict the value of the transmission for a car having fuel economy= 730/60 kmpl

1
0.5964291
> predict(model,newdata=econ,interval = "confidence")
fit lwr upr
1 0.5964291 0.3396301 0.8532281