Rental Car Fleet Size. The following data show the number of...

Rental Car Fleet Size. The following data show the number of rental cars in service (in thousands) for three rental car companies: Hertz, Avis, and Dollar over a three-year period (Auto Rental News website). Cars in Service (1000s) $$ \begin{array}{lcccc} \text { Company } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } & \text { Year 4 } \\ \text { Hertz } & 327 & 311 & 286 & 290 \\ \text { Dollar } & 167 & 140 & 106 & 109 \\ \text { Avis } & 204 & 220 & 300 & 270 \end{array} $$ a. Construct a time series graph for the years 2007 to 2010 showing the number of rental cars in service for each company. Show the time series for all three companies on the same graph. b. Comment on who appears to be the market share leader and how the market shares are changing over time. c. Construct a bar chart showing rental cars in service for 2010 . Is this chart based on cross-sectional or time series data?

Rental Car Fleet Size. The following data show the number of rental cars in service (in thousands) for three rental car companies: Hertz, Avis, and Dollar over a three-year period (Auto Rental News website).
Cars in Service (1000s)
$$
\begin{array}{lcccc}
\text { Company } & \text { Year 1 } & \text { Year 2 } & \text { Year 3 } & \text { Year 4 } \\
\text { Hertz } & 327 & 311 & 286 & 290 \\
\text { Dollar } & 167 & 140 & 106 & 109 \\
\text { Avis } & 204 & 220 & 300 & 270
\end{array}
$$
a. Construct a time series graph for the years 2007 to 2010 showing the number of rental cars in service for each company. Show the time series for all three companies on the same graph.
b. Comment on who appears to be the market share leader and how the market shares are changing over time.
c. Construct a bar chart showing rental cars in service for 2010 . Is this chart based on cross-sectional or time series data?

Key Concepts

Time Series Graph

A time series graph is used to display data points collected or recorded at specific, equally spaced time intervals. This type of graph helps in identifying trends, patterns, and seasonal variations in the data over time, making it an essential tool in time-dependent data analysis.

Data Visualization

Data visualization encompasses techniques for presenting data in graphical formats, such as line graphs, bar charts, and scatterplots, to aid in understanding complex information. Visual representation of data is crucial for making comparisons, revealing trends, and communicating findings clearly and effectively.

Market Share Analysis

Market share analysis involves examining a company's proportion of total sales or operational capacity within a particular market. By tracking changes over time, analysts can assess competitive positioning, identify market leaders, and understand shifts in consumer preference or industry dynamics.

Cross-Sectional and Time Series Data

Cross-sectional data is collected at a single point in time and provides a snapshot of a particular aspect, while time series data is gathered at multiple time points to show changes over time. Understanding the difference is critical in choosing the appropriate analysis method and in accurately interpreting the results from a given dataset.

Transcript

00:01 Hey everyone, today we're solving problem number 14 from chapter 1, section 2 of your textbook.

00:09 So let's jump right into it.

00:10 In part a, you're asked to draw a time series graph of the car sales for all three companies from 2007 to 2010.

00:18 So in time series graphs, when you're making them, the year or any, you know, the time element always goes on the y axes.

00:29 And then your number of cars in service, so i'll just write cars here.

00:32 Will always go, the other variable essentially will always go on the x -axis, i mean on the y -axis, whereas the time always goes on the x -axis.

00:42 So again, we have 07, 08, 09, and 0 -10, or just 10.

00:51 So i'm going to write that, 07.

00:54 Again, 07 is representative of the year 2007, 08 is representative of the year 2008, 2009 is representative of the year 2009 and finally one zero is the representative of the year 2010.

01:10 All right and then you look at your maximum value in terms of number of cars and service in thousands and for hertz it's somewhere above 300 but below 350 so i'm going to make a scale by 50 for this particular problem so again 350 ,000 cars and service is going to be my max for my y value on the scale at least not my max value i'm going to go up by 50 so 50 100 150 200 i went too small so 50 100 150 100 150 100 so i would have 50 and obviously this would be 100 100 100 100 100 150 would be here, then add another 50, you get to 200, and then you'd have 250 here.

02:09 So again, goes up by 50s.

02:11 All right, now it's time to graph.

02:13 I recommend making a key here, so write a key for your graph in part a at least.

02:20 And the reason for making a key is to kind of just show what different colors, if you're using different colors, when you're drawing the final answer, or different shapes.

02:30 So like if i had a star with different, instead of a dot, and then in like an x, the x would represent avis, the star represent hertz, you mean a dot or represent dollar, you can do something like that.

02:40 But since i have the colors on the swipe port, i'm going to utilize that.

02:44 So again, from my key for part a, i'm going to say anything red.

02:50 So a red dot or a red line is always going to indicate something about the hertz card company.

03:07 All right, then we'll say green.

03:10 So a green dot or a green line.

03:11 Would be indicative of values for avis and the line that we're going to make for avis.

03:19 And then, last but not least, i have blue.

03:23 So blue obviously has to represent, anything blue on my graph has to represent information regarding the dollar company for their cars and service from 2007 to 2010.

03:40 So now we're just basically going to graph the data.

03:43 For hertz, i can see that i'm going to have a graph that looks like this.

03:49 So a little bit above to 300, then a little bit below that, but still a lot of 300.

03:56 Then it dips below 300 in 2009, but then it picks back up just a little bit in 2010.

04:11 Again, straight lines.

04:12 Probably easier to do with a pen and paper.

04:17 And then we're moving on to avis.

04:20 Again, this is just grapping data points, guys.

04:23 So in 2007, avis had a little bit over 200 ,000 cars and service.

04:29 Then it went up in 2008, went not only above 250.

04:33 2009, it shot up close to 300.

04:43 And then o -10, it dipped below the hertz value.

04:47 But again, just by a little bit, not by too much.

04:50 So again, connect the dots with straight lines.

04:52 Best to make it straight.

04:55 And the beautiful thing about our keys, now we don't have to tell our, we already told our reader with our key what all our colors represent.

05:04 So with dollar, above 150, it started out in 07, then in 08, it dipped below 150, just minimally, i think.

05:18 09, dipped a lot, 10 picked up just to get a little bit, but very evenly spaced.

05:27 Not much just difference in 09 and 010 for a dollar.

05:30 So there you have it.

05:31 There's your time series graph.

05:33 Again, with time series graphs, you connect all your points with straight lines, and on the x axes, it's always going to be your time element.

05:40 Moving on to part p of the question, which asks us, for the first part, to figure out what the market share leader is in terms of number cars sold in thousands from 2007 to 2010.

05:59 So if i look at my graph, i see specifically that the red is leading the charge and the red is hertz...

Please give Ace some feedback