AP Stats Chapter 3

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21 Terms

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Response Variable

another term for dependent variable

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Explanatory Variable

another term for independent variable; a variable manipulated or observed by a research to explain the outcome variable in a statistical model.

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Scatterplot Description

D:Direction (positive, negative, or none)

UF: Unusual Features (outliers, clusters)

F: Form (linear or non-linear)

S: Strength (how close to the form) + CONTEXT

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Correlation - r

how closely the point follows a line

-1 = closer (negative slope)

1 = closer (positive slope) 

r value always between -1 and 1

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Interpreting R FRQ Explanation Example

The linear relationship between the number of rubber bands and the distance travelled is strong and positive.

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Interpreting R² FRQ Explanation Example 

97.4% of the variation in distance travelled is explained by the linear relationship with the number of rubber bands

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Interpreting Correlation

R**

direction (+ and -), form, and strength = between -1 and 1

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Interpreting Coefficient of Determination

R²**

“the percent of the variation in y explained by the linear relationship with x"

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Correlation vs. Causation

Correlation ≠ Causation

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Extrapolation 

*Be cautious w this

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Interpolation

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Predictions

ŷ = a + bx 

a = y-intercept 

b = slope 

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Residual

residual = actual - predicted

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Residual FRQ Explanation

The actual context was residual above/below the predicted value for x = #

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Interpretations 

When x = 0 context, the predicted y-context is y-int”

“for each additional x-context the predicted y context increases/decreases by slope”

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LSRL

Least Squares Regression Line = minimizes the sum of the sqaured residuals

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Residual Plots 

Good = sporadic spacing, no specific pattern

Bad = smile-shaped, u-shape, clear pattern

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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

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Outliers & the LSRL

  • Horizontal Outliers: tilt the line

  • Vertical Outliers: shift line up or down

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Transformations

Linear - Graph x vs. y

Exponential - Graph x vs. logy

Power - Graph logx vs. logy

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Choosing the best Regression Model 

  • Check the scatterplot for a linear pattern

  • Check the residual plot for no leftover pattern 

  • Check for the r² that is closest to 1