AP STATS: Unit 3 Review

Sampling Methods

Population: all individuals

• SRS:

  • random

  • good

• Convenience Sample:

  • NOT random

  • expertment choose

• Voluntary Response:

  • People choose

Stratified Random Samples:

• “Some of All"

• *Some members from all groups

Cluster Random Samples:

• “all of some”

• *all members from only some groups

Systematic Random Samples:

• choose a random starting point

• use regular intervals after

Potential Problems with Sampling

Undercoverage: when some members of a population can not be included or are left out

• EX. landline calls

Nonresponse bias: when a person or part of a sample chooses not to respond

Response bias: a pattern of inaccurate results

• EX. lying, wording questions, etc.

Least Squares Regression Lines, Predictions, & Residuals

Predictions

*be careful of extrapolation

Residuals

Resid + Actual - Predicted

y - ŷ

“The actual context was resid above/below the predicted for x=#.”

Slope

“For each additional x in context, we predict y in context increases/decreases by slope.”

Calculator Function: Residual Plot

• put x-values in L1

• put y-values in L2

• in L3: type your equation with L1 for x (for example: if equation is y = 1.6x + 5, type in 1.6*L1 +5)

• in L4: type L2 - L3 

• Go to Statplot menu - adjust your scatterplot settings so that XList: L1 and YList: L4

• Hit Graph and then Zoom 9

SAT PREP: Observational Studies & Experiments

Observational Study (NO treatment) vs. Experiments (treatment)

• Explanatory Variable (x): helps predict the response

• Response Variable (y): the outcome being measured

• Confounding Variable: variables that affect the response that have nothing to do with what you’re testing.

• Experimental Units: who/what is being tested

EX. design an experiment

s and r²

Standard deviation of residuals - s

Interpretation: “the actual (y in context) is typically (on avg.) about (s) unit away from the value predicted by the LSRL.”

Coefficient of determination - r²

Interpretation: "About (r²)% of the variability in (y in context) is accounted for by the LSRL.”

(r)² = r²

EX. r = .936, r² = (.936)²

Outliers and the LSRL

Outliers: out of pattern (large residuals)

High leverage: very large or very small x-values

Influential: if removed, big changes to slope, y-intercept, r

LT #1: Outliers and the LSRL

horizontal outliers → tilt the line

Vertical outliers → shift line up or down

• a good LSRL has low s + high r² (close to 1)