Scatter Plots and Correlation - Statistics and Econometrics - Lecture Notes, Study notes of Econometrics and Mathematical Economics

Scatter Plots and Correlation, Worksheets, Excel Workbook, Scatter, Correlation, Scatter Plot, Blank Columns, Top Toolbar, Chart Wizard, Input Range Box are some points from Statistics and Econometrics lecture notes.

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Scatter Plots and Correlation
Set-up: Open the data for this exercise
Open the data set called “baseball data” from the IMB 537 web page.
1. Insert 2 new worksheets and re-save the file as an Excel workbook with a new name on a different
disk (flash drive, desktop, etc).
2. Label the new sheets “scatter” and “correlation”.
A. Constructing a scatter plot for two variables:
1. Copy all data into the scatter sheet, then delete columns F L. We will not be using these variables
for this exercise.
2. Copy and paste the “ATTEND” column to the right of each of the other variables. You will have to
insert blank columns first (highlight the column where you want to put a new blank column, and click
“insert” then “column”). The new data set up should look like this:
POP
ATTEND
CAPACITY
ATTEND
PRIORWIN
ATTEND
CURNTWIN
ATTEND
TEAMS
ATTEND
4353
2704.794
52.806
2704.794
92
2704.794
104
2704.794
3
2704.794
2803
2110.009
43.737
2110.009
89
2110.009
89
2110.009
2
2110.009
9120
1821.815
57.545
1821.815
91
1821.815
87
1821.815
7
1821.815
2763
1661.618
33.583
1661.618
84
1661.618
86
1661.618
2
1661.618
2174
2045.784
53.197
2045.784
98
2045.784
85
2045.784
1
2045.784
...
3. On the main top toolbar, click the “chart wizard” icon (it looks like a small colorful bar graph).
4. Choose XY (scatter), and select the option on the right with no connecting lines, then click “next”.
5. With your cursor in the input range box, highlight the POP and ATTEND columns including labels,
and select the option for “series in columns”. Click “next”.
6. There are five tabs to choose from:
“Title” allows you to write in a title for your graph and put labels on the axes (you should title it
something like “POP vs. ATTEND”, and label the X axis POP and the Y axis ATTEND)
“Axes” allows you to specify the ranges for the values on the axes,
“Gridlines” allows you to have varying amounts of detail in gridlines, and
“Legend” simply places the chart legend at various positions in the graph.
Play with each of these and familiarize yourself with the options available, then when you’re
happy with what you have, click “next”.
7. The next box simply asks you where you want to put the chart either as a new sheet or embedded in
an existing sheet. Select an option, and then click “finish”. The completed chart should appear.
8. To change the size of the chart, simply click on its outside lines, and drag to a new size.
9. You can still go back and re-format any component of the chart. To format the axes (scale, font or
numbers), double click on the axis you want to format and a dialogue box will appear giving you
options. Try changing the scale of one of your axes and see how the chart changes. To format the
main plot area, double click in the main area. A different box with options will appear. To change
the data points (marker pattern or size), double click on any data point and change the options. For
example, the default marker is a triangle. Try changing this to a circle by double clicking a data
point, the selecting the pattern tab. You can change style and size, then click “OK”.
Repeat the above procedure for ATTEND and each other variable, so that you have a total of 5 scatter
plots. An important thing to note here is that we are assuming that attendance is dependent upon the other
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Scatter Plots and Correlation

Set-up: Open the data for this exercise Open the data set called “baseball data” from the IMB 537 web page.

  1. Insert 2 new worksheets and re-save the file as an Excel workbook with a new name on a different disk (flash drive, desktop, etc).
  2. Label the new sheets “scatter” and “correlation”.

A. Constructing a scatter plot for two variables:

  1. Copy all data into the scatter sheet, then delete columns F→ L. We will not be using these variables for this exercise.
  2. Copy and paste the “ATTEND” column to the right of each of the other variables. You will have to insert blank columns first (highlight the column where you want to put a new blank column, and click “insert” then “column”). The new data set up should look like this:

POP ATTEND CAPACITY ATTEND PRIORWIN ATTEND CURNTWIN ATTEND TEAMS ATTEND 4353 2704.794 52.806 2704.794 92 2704.794 104 2704.794 3 2704. 2803 2110.009 43.737 2110.009 89 2110.009 89 2110.009 2 2110. 9120 1821.815 57.545 1821.815 91 1821.815 87 1821.815 7 1821. 2763 1661.618 33.583 1661.618 84 1661.618 86 1661.618 2 1661. 2174 2045.784 53.197 2045.784 98 2045.784 85 2045.784 1 2045. … … … … … ... … … … …

  1. On the main top toolbar, click the “chart wizard” icon (it looks like a small colorful bar graph).
  2. Choose XY (scatter), and select the option on the right with no connecting lines, then click “next”.
  3. With your cursor in the input range box, highlight the POP and ATTEND columns including labels, and select the option for “series in columns”. Click “next”.
  4. There are five tabs to choose from: “Title” allows you to write in a title for your graph and put labels on the axes (you should title it something like “POP vs. ATTEND”, and label the X axis POP and the Y axis ATTEND) “Axes” allows you to specify the ranges for the values on the axes, “Gridlines” allows you to have varying amounts of detail in gridlines, and “Legend” simply places the chart legend at various positions in the graph. → Play with each of these and familiarize yourself with the options available, then when you’re happy with what you have, click “next”.
  5. The next box simply asks you where you want to put the chart – either as a new sheet or embedded in an existing sheet. Select an option, and then click “finish”. The completed chart should appear.
  6. To change the size of the chart, simply click on its outside lines, and drag to a new size.
  7. You can still go back and re-format any component of the chart. To format the axes (scale, font or numbers), double click on the axis you want to format and a dialogue box will appear giving you options. Try changing the scale of one of your axes and see how the chart changes. To format the main plot area, double click in the main area. A different box with options will appear. To change the data points (marker pattern or size), double click on any data point and change the options. For example, the default marker is a triangle. Try changing this to a circle by double clicking a data point, the selecting the pattern tab. You can change style and size, then click “OK”.

Repeat the above procedure for ATTEND and each other variable, so that you have a total of 5 scatter plots. An important thing to note here is that we are assuming that attendance is dependent upon the other

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variables. This is why we put ATTEND to the right of each of the other columns – excel always puts the variable on the right on the Y axis.

Question: Do you see any outliers in the data? What types of relationships do you observe between these variables?

Part VI. Correlation We’re going calculate the correlation coefficients for all combinations of the 4 variables used above.

  1. Copy and paste all data into the correlation sheet, then delete columns F→ L.
  2. Click “Tools” , then “Data Analysis” then “Correlation”, then “OK”
  3. In the input range box, highlight all 6 columns of data, including the labels
  4. Check the circle for “Grouped by: Columns”
  5. Check the “labels in first row” box
  6. Select an output range and click “OK”

Your output should consist of a 6 x 6 matrix. The correlation coefficient between two variables is found in the corresponding off-diagonal element of the matrix.

Questions: How would you describe the strength and direction of each of the relationships? Do these coefficients back-up your scatter plots?

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