AP Statistics Unit 2 Vocab Review
How do you interpret the standard deviation of residuals?
"The actual (y-context) typically varies by about (S) from the value predicted by the LSRL."
How do you interpret the y-intercept for an LSRL?
"When (x = 0 context), the predicted (y-context) is (y-intercept)."
How do you interpret the slope for an LSRL?
"With each additional (x-context), the predicted (y-context) will (inc./dec.) by (slope)."
What does a good LSRL have?
A good LSRL has a low S and a high r squared.
What acronym should you use when asked to "describe the relationship" displayed in a scatterplot (2 Variable data)?
D: Direction (positive or negative) U: Unusual Features F: Form (linear or non-linear) S: Strength (how close does it fit to a line or curve?) + CONTEXT
Define explanatory vs response variables.
Explanatory variables are used to predict something (x), while response variables are the result of a prediction (y).
How do you use the Least-Squares Regression Line?
Go to Stat -> Calc -> 8: LinReg a+b(x) - when writing the LSRL, put a "hat" over the y to indicate that the formula is for predictions and not exact.
What is r and how do you interpret it?
R is the strength of a correlation, and 1 and -1 are both strong positive and negative correlations, respectively. 0 is a weak correlation. - r has no units - swapping x and y doesn't change the correlation - NON-resistant to outliers Interpret with direction (pos or neg) and strength (i.e. moderately, slightly, strongly)
What does r squared tell us and how do you interpret it?
R squared tells us how well the LSRL is at making predictions. interpret: "About (r squared)percent of the variation in (y-context) can be explained by the LSRL."
What is the formula for residuals?
Residual = Actual - Predicted Interpret: "The actual (y-context) was (residual #) (above/below) the predicted value for (x = #)."
What does the LSRL minimize?
The LSRL minimizes the sum of the squared residuals.
Which outliers have the greatest impact on the LSRL, vertical or horizontal outliers?
The horizontal outliers affects both slope and LSRL. They are called "high leverage points" or "influential points" (if removed, significantly changes the slope, y-int., or correlation). *Think of the LSRL as a see-saw!
How do you know if a residual plot is a good fit?
The residual plot should have no pattern, it should be randomly scattered.
Define extrapolation.
To predict values outside of the given data. *DON'T DO THIS
What must you do to your calculator when needing to find r (correlation)?
Turn ON your diagnostic and turn ON your Stat plot.
Extra formulas for LSRL.
b = r * (Sy/Sx) a = y-bx
