unit 3 AP stats

how to interpret slope: “The predicted y goes up/down by about b for each increase of 1 unit in X.”

how to interpret the y-intercept of a regression line: “The predicted is __ is about_ when __ is 0.”

How to interpret residual: “The actual__ is__ more/less than the value predicted by the regression line using x=__".”

residual = Actual-predicted

residual= y-ŷ

residual=prediction error of equation of the least Squared Regression Line

Describing scatterplot: Form-is a line an appropriate model? Association-positive or negative trend(to the right). Strength- correlation is useful for linear models. unusual features- clusters, points far away from others.

Correlation is not resistant to outliers because it uses mean and SD
Correlation: close to 1 or -1= strong correlation. close to 0=weak association

Correlation has no units.

general for of a regression equation: ŷ=a+bx

ŷ=predicted value from the model

y=actual observed value

extrapolation is using a model to make predictions outside the range of observed inputs.

The best-fit regression line for a set of data: minimizes the sum of the squared residuals. Added up equal residual.

to find the equation of the least squares regression line: b=r Sy/Sx. a=ybar-b(xbar)

residual plot: plots the x list vs the residual(error) for each input. helps determine if a line is the best model to use

linear model appropriate?: no pattern-linear model is good. pattern-line might not be the best fit

S is the typical prediction error

s: “Prediction made using this linear model typically vary by about S units from the actual y.”

compare sum of squared residuals: 1. sum of squared error from the line that just uses the mean. 2. sum of squared errors from the least squared regression equation line

r² measures how much better the sum of squared errors from the least squared regression equation line is than the sum of squared errors from the line that uses mean.

Interpet r²: “__% of the variability in__ is accounted for by the least squared regression line with x=__.”

r=√R²

r² and s both measures how well a line fots the data, just in different ways.