AP Statistics / Mr. Hansen
10/26/2005

Name: _________________________

Answer Key for Big Quiz, 10/14/2005

 

16.

. . . the difference is too large to be plausibly explained by chance alone.

17.

This is a “post hoc, ergo propter hoc” fallacy. The mere fact that a drop in crime rate occurred after the sheriff rose to power does not allow us to conclude that his policies caused the drop. Correlation does not imply causation!

18.

LSRL residuals always add up to 0. These clearly do not, since their sum is obviously negative.

19.(a)

x = speed (in mph) = explanatory variable
y = wake horsepower (in hp) = response variable

(b)

This model is inappropriate for several reasons.

  • LSRL predicts negative horsepower (nonsense) for speeds below about 15 mph. [It is helpful to provide a scatterplot with LSRL overlaid to illustrate this statement.]
  • Residual plot [must be sketched for full credit] shows clear “bowl-shaped” pattern, suggesting that a power or exponential fit would be better.
  • The y-intercept should be 0, or close to 0, not –172.529 hp.

(c)


[Note: Work as shown, including final answer with units of hp shown, would be required for full credit.]

(d)

–172.529 = predicted wake hp when speed is 0 mph

(e)

11.458 = the predicted # of addl. hp needed for each addl. mph of speed

(f)

r = .837 = linear correlation coefficient [all 3 words required for full credit]
r2 = .701 = coefficient of determination