MATH 1342. Chapter 5. Mary Parker Feb. 5, 2013
Chapter 5, Day 2
page 1
(Link to MANY resources in the Detailed Course Calendar.)
1. Interpret coefficients of regression line: Slope and y-intercept.
2. Compute the equation of the regression line by hand and use it to predict y when x is a given
value.
3. Use software to do MANY computations.
4. Regression Facts. (1, 2, 3, 4.)

The hardest to understand is Fact 4 about r 2 . The value r 2 is the variation in y that is
explained by the variation in x. Another way of thinking about that is that r 2 tells us
how good the regression predictions are when compared to the predictions we would
have without doing regression.
5. Residual plots.

If the residual plot against the explanatory variable appears randomly scattered around
a center line at 0, that is an indication that the data are well-described by the regression
model.
6. Influential Observations.

These play a similar role to that of outliers in the one-variable problems. An
observation can be influential for correlation or influential for regression, or neither, or
both. We don’t have a strict criterion for what makes it influential or not in each case.
Just do the required computations and say whether it seems that the results are very
different. If they are, then the observation is influential in that context.
7. Cautions.
a. Correlation and regression only describe linear relationships, not other types of
relationships.
b. Correlation coefficient and regression lines are not resistant.
c. Correlations between averages are usually much stronger than correlation among
individuals.
d. Beware of extrapolation.
e. Lurking variables make it hard to determine the results of a study.
f.
Association does NOT imply Causation.