4.2 – Linear Regression and the Coefficient of Determination Sometimes we will need an exact equation for the line of best fit. Vocabulary Least-Squares.

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Presentation transcript:

4.2 – Linear Regression and the Coefficient of Determination Sometimes we will need an exact equation for the line of best fit. Vocabulary Least-Squares Criterion Least Squares Line – Equation

Least-Squares Criterion The sum of the squares of the vertical distances from the data points (x, y) to the line is made as small as possible.

Least-Squares Line

Additional Vocabulary The slope tells us how many units the response variable is expected to change for each unit change in the explanatory variable. (Marginal change) Interpolation: predicting ŷ values for x values that are between observed x values in the data set. Extrapolation: predicting ŷ values that are beyond observed x values.

Guided Exercise #3 As whole group, turn to page – Look-over answers – Whole group clarification

Correlation Coefficient … r Numerical measurement that assesses the strength of a linear relationship between two variables x (explanatory) and y (response). -1 ≤ r ≤ 1 – Positive/Negative – like slope – r = 1 or -1 : perfect linear correlation (line) – r = 0 : no correlation (can’t make line) Same if we switch x and y: (x,y) = (y,x)

Correlation Coefficient … r

Guided Exercise #4 As whole group, turn to page 146 – Look over answers – Whole group clarification

Checkpoint  Make a scatter diagram  Visually estimate the location of “best-fitting” line for scatter diagram  Use sample data to compute the sample correlation coefficient r  Investigate meaning of r

Homework Read Pages – Take notes on what we have not covered Do Problems – Page (1-11) Check odds in back of book Check all on website Get Ready for Test Chapter Review Problems Notes/vocab