It is important to look at data in a graphical form. Patterns are the
essence of data exploration, and the eye’s ability to discern forms and
patterns makes visual display integral to the process. The visual
display of quantitative information can help us see connections and
relationships in the data, which are oftentimes difficult to detect in
tables of numbers. We should look at data in a graphical form, and not
rely solely on computational or statistical metrics.
In this discussion, we will explore graphs in linear regression. Our
data are taken from an article by Frank Anscombe in a 1973 article in The American Statistician, which discusses scatterplots in relation to regression analyses.
First, download the dataset MHA610_Week 5_Discussion_Regression_Data.xls.
This is a simple Excel workbook, with data on one sheet. There are
eight columns of data, with headings X1, Y1, X2, Y2, X3, Y3, X4, Y4.
Import the data into Statdisk using the MHA610_Week 5_Discussion_Regression_Data.CSV file, and perform the following analyses.
- Calculate the regressions of Y1 on X1, Y2 on X2, Y3 on X3, and
Y4 on X4, and compare the results (summary statistics). Explain what, if
anything, you find unusual about these results.
- Plot each set of data, along with the fitted regression line.
Describe what the graphs tell you about the relationships between the
X’s and the Y’s.
- Explain what lessons you draw from this exercise.
Place the summary statistics and the plots in a separate Word document
and attach that document to your initial post. Address the questions in
the body of your initial discussion post.