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Response Variable
another term for dependent variable
Explanatory Variable
another term for independent variable; a variable manipulated or observed by a research to explain the outcome variable in a statistical model.
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
Correlation - r
how closely the point follows a line
-1 = closer (negative slope)
1 = closer (positive slope)
r value always between -1 and 1
Interpreting R FRQ Explanation Example
The linear relationship between the number of rubber bands and the distance travelled is strong and positive.
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
Interpreting Correlation
R**
direction (+ and -), form, and strength = between -1 and 1
Interpreting Coefficient of Determination
R²**
“the percent of the variation in y explained by the linear relationship with x"
Correlation vs. Causation
Correlation ≠ Causation
Extrapolation
*Be cautious w this
Interpolation
Predictions
ŷ = a + bx
a = y-intercept
b = slope
Residual
residual = actual - predicted
Residual FRQ Explanation
The actual context was residual above/below the predicted value for x = #
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”
LSRL
Least Squares Regression Line = minimizes the sum of the sqaured residuals
Residual Plots
Good = sporadic spacing, no specific pattern
Bad = smile-shaped, u-shape, clear pattern
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
Outliers & the LSRL
Horizontal Outliers: tilt the line
Vertical Outliers: shift line up or down
Transformations
Linear - Graph x vs. y
Exponential - Graph x vs. logy
Power - Graph logx vs. logy
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