AP Statistics Chapter 8- Linear Regression
The LSRL passes through which point?
(mean of x, mean of y)
What conditions are necessary before using a linear model for a set of data?
-Straight/Linear enough -Check for outliers
The R^2 value shows how much of the variation in the response variable can be accounted for by the linear regression model. If R^2 = 0.95, what can be concluded about the relationship between x and y?
95% of the variability in Y is accounted for by the linear relationship with X.
Residual
Difference between observed value and associated value.
How many residuals does a set of data have?
Equal to the number of points a set of data has.
Predicted Value
Estimate made from a model. ŷ
R-squared
Fraction of data's variance accounted for by the model.
What is a residual and how is it calculated?
How far a piece of data is from the best fit line. Calculated by subtracting predicted value from observed value.
Explain how to construct a residual plot.
In a calculator go to STAT EDIT and put the plots under RESID. Set up a STATPLOT Plot 2 as a scatterplot with Xlist:YR and YLIST:RESID. Go to Y= screen and hit ENTER and turn off the regression line and Plot1 and turn on Plot2. ZoomStat.
What is meant by a least squares regression line?
Line for which the sum of the squared residuals is the smallest.
Coefficient of determination
Measures the success of the regression model in terms of the fraction of the variation of Y accounted for by the regression.
What does a negative residual indicate? A positive residual? A residual of 0?
Negative-Model's prediction too high Positive-Model's prediction too low 0-Prediction matched observed value
If a least-squares regression line fits the data well, what characteristics should the residual plot exhibit? Sketch a well-labeled example.
Should be in horizontal direction, shapeless form, roughly equal scatter for all predicted values.
Describe the difference between the two types of Y.
Y-Real life value ŷ Y-Predicted value on line of best fit
