Tips - Quiz #4
- Readings (from SAS text):
- Chapter 9: Section on "Performing Straight-Line Regression". That is pp289 - pp298.
On page 296 read the subsection "Variable, Parameter Estimate" only.
Skip pp297. On page 298 read the subsection "R-square" only (skip
the first two sentences).
- Chapter 10: pp337 - pp339
- Chapter 4: Section on "Box Plots. That is pp111
- Important Points:
- You should be able to state the regression model. Remember the model includes the assumptions.
- You should understand how to read the output of PROC REG.
Remember that you are only interested in the entries under the heading
"Parameter Estimate" and the entry beside "R-square" (see reading).
- You need to know how to interpret the "R-square" entry (see reading).
- You need to know how to determine the correlation coefficient from R-square.
That is, it is given by the square root of R-square but its sign is determined by the sign of the estimate of the slope parameter.
For the PROC REG output above, the R-square value is 0.8677 and the sign of the
slope of the regression line is positive.
Hence, the correlation coefficient is +sqrt(0.8667) which is 0.931.
- You need to know how to evaluate model assumptions:
- Residuals have mean zero for fixed x: Check the
box plot for outliers (see reading). Outliers are
points identified by '0' or '*' beyond the whiskers. The presence ot outliers
indicates that this model assumption is invalid.
- Residuals have constant standard deviation for fixed x: Check the residual plot. Remember to focus your attention on
the middle two thirds of the plot and compare the spread at each extreme.
- Residuals drawn from a Normal population:
Check the normal plot (apply the pen test) and
the p-value of the normal test. Remember that a p-value
greater than 0.05 indicates that there is insufficient evidence to reject Ho
while a p-value less than or equal to 0.05 indicates that Ho should be rejected
in favor of Ha.
You also need to know the associated hypotheses for the normal test:
Ho: Residuals are drawn from a normal distribution
Ha: Residuals not drawn from a normal distribution