## Homework 2

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This homework is due on Feb. 3, 2020 at 12:00pm. Please submit as a PDF file on Canvas.

This homework uses the Cars93 data set. Each observation in the data frame contains information on passenger cars from 1993. This is a big data frame with 27 columns. We are interested in the information on manufacturer (Manufacturer), car model (Model), type of car (Type), midrange price in $1000 (Price), maximum horsepower (Horsepower), drivetrain (DriveTrain), and city MPG (miles per US gallon, MPG.city). Cars93 <- read.csv("http://wilkelab.org/classes/SDS348/data_sets/Cars93.csv") head(Cars93) ## Manufacturer Model Type Min.Price Price Max.Price MPG.city ## 1 Acura Integra Small 12.9 15.9 18.8 25 ## 2 Acura Legend Midsize 29.2 33.9 38.7 18 ## 3 Audi 90 Compact 25.9 29.1 32.3 20 ## 4 Audi 100 Midsize 30.8 37.7 44.6 19 ## 5 BMW 535i Midsize 23.7 30.0 36.2 22 ## 6 Buick Century Midsize 14.2 15.7 17.3 22 ## MPG.highway AirBags DriveTrain Cylinders EngineSize ## 1 31 None Front 4 1.8 ## 2 25 Driver & Passenger Front 6 3.2 ## 3 26 Driver only Front 6 2.8 ## 4 26 Driver & Passenger Front 6 2.8 ## 5 30 Driver only Rear 4 3.5 ## 6 31 Driver only Front 4 2.2 ## Horsepower RPM Rev.per.mile Man.trans.avail Fuel.tank.capacity ## 1 140 6300 2890 Yes 13.2 ## 2 200 5500 2335 Yes 18.0 ## 3 172 5500 2280 Yes 16.9 ## 4 172 5500 2535 Yes 21.1 ## 5 208 5700 2545 Yes 21.1 ## 6 110 5200 2565 No 16.4 ## Passengers Length Wheelbase Width Turn.circle Rear.seat.room ## 1 5 177 102 68 37 26.5 ## 2 5 195 115 71 38 30.0 ## 3 5 180 102 67 37 28.0 ## 4 6 193 106 70 37 31.0 ## 5 4 186 109 69 39 27.0 ## 6 6 189 105 69 41 28.0 ## Luggage.room Weight Origin Make ## 1 11 2705 non-USA Acura Integra ## 2 15 3560 non-USA Acura Legend ## 3 14 3375 non-USA Audi 90 ## 4 17 3405 non-USA Audi 100 ## 5 13 3640 non-USA BMW 535i ## 6 16 2880 USA Buick Century Problem 1: (3 pts) Use ggplot2 to create a scatter plot of maximum horse power versus car price. In the same plot, fit a curve to these data using geom_smooth(). In 1-2 sentences, what broad trend do you observe in horsepower for different car prices? HINT: Plot maximum horse power on the y-axis and price on the x-axis. ggplot(Cars93, aes(x = Price, y = Horsepower)) + geom_point() + geom_smooth() ## geom_smooth() using method = 'loess' and formula 'y ~ x' Horsepower generally increases with price until$40,000, and then appears to level off after. However, there are few data points for cars costing more than \$40,000.

Problem 2: (3 pts) Next, create a scatter plot of horsepower against city MPG, facetted by type of drivetrain. In 1-2 sentences, make one observation about the data from this plot.

ggplot(Cars93, aes(x = Horsepower, y = MPG.city)) +
geom_point() +
facet_wrap(~DriveTrain)

Observations:

1. City MPG and horsepower are negatively correlated (i.e., as city MPG goes up, horsepower goes down)

2. Cars that are rear-wheel drive have the lowest MPG city.

3. Front-wheel drive cars have the highest MPG city.

4. All three types of drivetrains have similar ranges of maximum horsepower (100-300HP).

Problem 3: (2 pts) Plot the distribution of car price, once using geom_histogram() and once using geom_density().

ggplot(Cars93, aes(x = Price)) +
geom_histogram()
## stat_bin() using bins = 30. Pick better value with binwidth.

ggplot(Cars93, aes(x = Price)) +
geom_density()

Problem 4: (2 pts) What does the y-axis in your histogram represent? In your density plot, what is the total area under the curve? Please give a single number as your answer. HINT: You do not need to do any additional calculations to determine the area under the curve. Use Google to find the answer.

The y-axis in a histogram represents counts in a given range of x-values (bins). The area under the curve of a density plot always sums to 1.