Stat 112: Correlation, LS, Extrapolation

• Administrivia:
  • Sample homework problems are listed on schedule along with the reading. You should do both to keep from following behind in the class.

• Measuring the degree of association
  • Positive and negative LINEAR associations are measured by correlation
  • Perfectly postive = +1, perfectly negative = -1, no association = 0 (see page 130 for pictures)
  • Nice property: scale independent (try Y=chance of snow, X=temp)
  • Bad property: scale independent! (Y = MPG, X = engine size)
  • Called r

• What if it isn't linear
  • Tukey's "bulging rule"
  • Draw a circle, divide into 4 pieces
  • Upper left: sqrt X, log X, 1/X, Y²
  • Upper right: X² Y²
  • Lower left: sqrt X, log X, 1/X, sqrt Y, log Y, 1/Y
  • Lower right: X², sqrt Y, log Y, 1/Y
  • So transform data then do analysis
  • Example: Boat price vs boat length

• Which line to use for a blob of points?
  • Suppose X and Y aren't related (i.e. correlation = 0)
  • Try both flat and 45 degree line--both seem to fit equally well
  • Think about prediction though. If you wanted a large Y, would you be better off picking a small X or a large X?
  • This is what the LS line tries to answer
  • Observed = predicted + error. Draw a picture! (or see p 140)
  • r = visual LS slope

• Equation for LS line
  • Centercept: (X-bar, Y-bar)
  • slope: b = r s_Y/s_X
  • predicted y = a + b x

• Extropolation
  • Good life: small error in slope = big error in prediction
  • Bad life: linear doesn't even hold
  • Blood presure = 70 + age / 2
  • What is blood presure at age 1000? (prediction = explosion, truth = 0!)

• Use a computer!
  • It is more important to get a computer to do the above for you than to be able to do it in your head.
  • Use JMP IN to do some of the homework.

Last modified: Thu Jan 20 09:14:25 EST 2000