Interesting Diversion: You will find a number of different regression expressions in the STAT CALC
menu: LinReg(ax+b), QuadReg, CubicReg, QuartReg, LinReg(a+bx), LnReg, ExpReg,
PwrReg, Logistic , and SinReg . While each of these has its use, only LinReg (a+bx) needs to be
used in this course (well, LinReg (ax+b) gives the same equation—with the a and b values reversed,
just in standard algebraic form rather than in the usual statistical form).Exam Tip: Also remember, when taking the AP exam, NO calculatorspeak. If you do a linear
regression on your calculator, simply report the result. The person reading your exam will know that
you used a calculator and is NOT interested in seeing something like LinReg L1,L2,Y1 written on your
exam.It may be worth your while to try several different transformations to see if you can achieve linearity.
Some possible transformations are: take the log of both variables, raise one or both variables to a power,
take the square root of one of the variables, take the reciprocal of one or both variables, etc.
Rapid Review
The correlation between two variables x and y is 0.85. Interpret this statement.
Answer: There is a strong, positive, linear association between x and y . That is, as one of the
variables increases, the other variable increases as well.
- The following is a residual plot of a least-squares regression. Does it appear that a line is a good
model for the data? Explain.
Answer: The residual plot shows a definite pattern. If a line was a good model, we would expect to
see a more or less random pattern of points about 0. A line is unlikely to be a good model for this
data.
Consider the following scatterplot. Is the point A an outlier, an influential observation, or both? What
effect would its removal have on the slope of the regression line?