AP statistics unit 2

describing scatter plots

direction (positive/negative), form (linear/curved), strength, unusual features

scatterplot on calculator

Stat -> Edit, then 2nd -> Statplot

r

correlation coefficient

r measures

the strength of correlation between two quantitative variables

conditions of r

quantitative, straight enough, no outlier

r²

coeffiricent determination

r² measures

how much of the variation in the y-variable is explained by variation in the x-variable

lurking variable

a variable that could cause changes in x and y that’s not measured

residual

the vertical distance between the point and the line of best fit. Actual – Predicted

line of best fit on calculator

type x’s into L1, y’s into L2. Then, Stat-CALC-8:LinReg(a+bx). If the output says: 𝑦 = 𝑎 + 𝑏x; 𝑎 = 2.3; 𝑏 = 1.1, then the line of best fit is 𝑦 = 2.3 + 1.1x

lie of best fit slope =

r * (SD of y/SD of x)

lie of best fit y-intercept =

mean of y - (mean of x * slope)

regression to the mean

number of SD * r = actual prediction from mean

residual plot on calculator

fter data is entered in L1 and L2, do Stat -> CALC -> 8:LinReg(a + bx).
Then, 2 nd ->Statplot, select Scatterplot. Change the Y-List to RESID by highlighting it and clicking 2 nd -> STAT -> RESID. Then, ZOOM -> 9.

residual plot is random

plot is linear, otherwise probably curved

extrapolation

predicting data beyond domain

influential outlier

point changes r or line of best fit

high leverage

far horizontally

high residual

far vertically

re-expression if

scatter plot is not straight enough

re-expression on calculator

1) Sketch a scatterplot of data. (Straight line = good)
2) Do linear regression on it. Record r and r 2 (r close to 1 or -1 = good. r 2 close to 1 = good)
3) Sketch the residual plot. (Random scatter = good)
4) Take the square root of the y’s and store as a new list √ L2 STO L3
5) Now, redo steps 1-3, using L1 and L3
6) Continue transforming L2 using Log(y), stored in L4, 1/√𝑦, stored in L5, and 1/𝑦 ,
stored in L6, in that order, and keep repeating steps 1-3. If those all fail, try Log(x)
and y, or Log(x) and Log(y)
o On calc: Log L2 STO L4
o On calc: 1/ √ L2 STO L5
o On calc: 1/L2 STO L6
7) Choose which one works best by checking the scatterplot, r,r², and the residual plot
8) Make predictions with your old x's and new y's

graph oscillates

can’t re-express if