Fathom Tutorial
We will be using the cars and trucks data in fathom to produce appropriate two variable graphs for each of the variables in the data set. There are
____variables; choosing two variables at a time would yield ______ different combinations of variables! We will examine only a few. Copy and paste your
graphs and tables into a word processing document as your progress through the tutorial. Use textboxes to makes any comments about noticeable trends from
the graphs and tables as prompted (in bold) throughout the tutorial.
Launch Fathom and open the cars and trucks data set and open the inspector.
Recall that discrete variables can be treated like categorical variables when you hold the shift key down, otherwise discrete variables will be handled the same
way as continuous variables.
CATEGORICAL VS CATEGORICAL:
Example 1: Categorical vs. Categorical on the SAME axis: Drag the graph icon to the work area. Drag Domestic vs. Foreign to the x-axis. Since there are
more foreign vehicles than domestic, the results should be expressed as a percentage. To change to percent, change count( ) to To compare this
variable to another categorical variable, drag any Rating attribute to the x-axis holding the shift key down drop this attribute to the PLUS sign that appears
on x-axis. What differences in ratings do you notice amongst the two origins?
Example 2: Categorical vs. Categorical on OPPOSITE axis: Drag the graph icon to the work area. Drag Domestic vs. Foreign to the x-axis. Drag one of the
rating attributes to y-axis (hold shift key down). Using the pull down menu on the top right corner of the graph change the bar chart to a breakdown plot.
Each point represents one vehicle. The observed points are broken down by both attributes. Comment on the results.
Example 3: Numerical Summaries for Categorical vs. Categorical: Observed vs. Expected Tables
Bring down a summary table to the workspace. Drag Domestic vs. Foreign to the top of the table. Drag one of the rating attributes to the side of the table,
while holding down the shift key. The observed quantities are broken down by both attributes. How many Domestic cars have a 5 star rating? How many
foreign cars have a 5 star rating?
Add a formula to the table, type in expected in the formula editor. The values are a result of the product of the row total with column total divided by the
grand total. These values represent the quantities that would be expected if there were no difference between Domestic and Foreign cars. Do any expected
values deviate from the observed values?
CONTINUOUS VS. CONTINUOUS:
Example 4: Continuous vs. Continuous on the SAME axis: Drag the graph icon to the work area. Drag the any Rating attribute to the x-axis (do not hold down
the shift key this time). Change the graph to a box plot. Now, one at a time drag the other two rating variables to the plus sign on the x-axis.
Repeat this process in a new graph for CityMPG and HwyMPG.
Example 5: Continuous vs. Continuous on the OPPOSITE axis. Drag the graph icon to the work area. Drag the MSRP attribute to the x-axis. Drag the 5 Year
Resale Value attribute to the y-axis. Fathom creates a scatter plot of the data. Right click on the plot and add a least squares line. Below the graph the line of
best fit is shown in the form y = mx + b, as well as a statistic, r 2, called the coefficient of determination (ignore this for now). Interpret the relationship and
the rate of change between the variables. As ________(the independent variable) increases _______ (the dependent variable)
_______(rapidly/moderately/gradually)______(increases/decreases) at a rate of _________(slope as a rate of change).
Duplicate this graph. Drop the Domestic vs. Foreign attribute to the center of the graph. This should show split the points and the least squares lines
according to origin. Compare the two lines of best fit.
Create another scatter plot using Weight and CityMPG. Which Attribute is the dependent variable?
The Scatter plot is non-linear, so a line of best fit is not applicable. Applying a transformation to the data often adjusts for non-linearity in the data. To do
this create a new variable called reciprocal weight using the formula . Make another scatterplot of CityMPG with reciprocal weight. Create a line of best
fit using the least squares line.
Create a scatter plot for MSRP vs. City MPG. Drop HwyMPG to the plus sign on the x-axis, to create a scatter plot showing the relationship between MPG and
MSRP. Describe this relationship.
Example 6: Numerical Summary. In a summary table drag weight to the top and length to the side or vice versa, the correlation is calculated. We will discuss
this statistic later.
CONTINUOUS VS. CATEGORICAL (can only be on opposite axis)
Creates a Continuous type graph or statistics split by the Categorical variable.
Example 7: Numerical Summary. Drag a summary table to the workspace. Drop Percentage Decrease in Value to the top of the table; drag Markup to the top
arrow and Domestic vs. Foreign to the side of the table. Add the median to the table. Compare the results.
Example 8: Graph. Drag the graph icon to the workspace. Drag MSRP to the x-axis. Drag Domestic vs. Foreign to the y-axis. Change the graph to a histogram.
Example 9. Creating new Collections. We can create a scatter plot for continuous vs. discrete variables by following these steps: Create a summary table for
with MSRP at top of the table and any rating attribute to the side of the table (hold shift key down). Add a formula for the median to the table and cut the
other formulas that appeared by default. Making sure only the median is displayed in your summary table, right click on your table and Create collection from
cells. With the created collection selected, bring a collection table down. This table displays the data from the new collection that was created. In this
collection table, rename S1 as “Average MSRP”. Make a scatter plot of Average MSRP vs. Rating. Describe the relationship.