Regression Lab In StatCrunch
Lab 3: Regression, Correlation and Outliers
- We are going to work with the small diamonds data set again, accessible here: diamonds3K sampled from a larger data set with Codebook.
- We are going to look at the three dimensions of diamonds and how they covary: length (x), width (y), and height (z).
- Make a scatter plot for (x versus y) and separately for (x versus z).
- One of the conditions for correlation and regression is the "No outliers condition."
- Do you see outliers in the plots?
- Click on an outlier to turn it pink.
- Is the outlier an outlier for the other relationship? (x versus y) versus (x versus z). The dot on the other scatter plot also turns pink.
- Look at the row in the data set for each outlier. To find the row, press one of the arrows on the pink box that appeared on the lower left.
- Can you tell if the data were recorded wrong or if the diamond really had those dimensions? Consider what x, y, and z mean and remember you also have a measure of the diamond's weight (carat). Plot scatter plots with carat and x, y or z, and discuss.
- Repeat for the other most extreme outliers.
- Plot the Residuals versus "X-Values" (explanatory variable), a histogram of the residuals, and a QQ-Plot of the residuals. Where does the outlier(s) show up? With the outliers removed, is a simple-linear regression analysis appropriate?
- Report the correlation coefficient and regression line with the outliers and without the outliers (see below).
- To do the analyses without the outliers, use Stat, Regression, Simple Linear to Save Residuals, then use a "where" function to restrict the data to points with small enough residuals.