Chapter 4: Correlation and Regression 4.1 – Scatter Diagrams and Linear Correlation 4.2 – Linear Regression and the Coefficient of Determinant

Focus Problem “Changing Populations and Crime Rate” Read page in text book

4.1 – Scatter Diagrams and Linear Correlation Studies of correlation and regression of two variables usually begins with a graph of paired data values (x, y). Vocabulary Scatter diagram – Explanatory variable – Response variable Correlation Lurking variable Line of “best fit”

Scatter Diagram Graph where data pairs (x, y) are plotted as individual points on a coordinate plane – Explanatory Variable: the X variable – Response Variable: the Y variable

Scatter Diagram Possible to draw curves to get close to data, but straight lines are simplest and widely used in basic statistics. “Best-Fitting Line” – Comes closet to each of the points of scatter plot More exact in 4.2 – Sometimes doesn’t make a good line No linear correlation – Curves, too spread out

Guided Exercise #1 As whole group, turn to page – Look-over answers – Whole group clarification – Graphing Calculator

Scatter Diagram Looking at a scatter diagram to see whether a line best describes the values of a data pair, and seeing a relationships between the two variables (explanatory and response) is important. Sample correlation coefficient: “r”

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 #2 As whole group, turn to page 129 – How did we do? – Whole group clarification – Graphing Calculator

Cautions about Correlations r = sample correlation coefficient ρ = population correlation coefficient – Greek letter “rho” Causation: – Lurking variables: may be responsible for changes in explanatory or response variables.

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 (1-16) Check odds in back of book Check all on website Read and preload 4.2 information – Notes/vocab