Chapter 4: Correlation and Regression

4.1 – Scatter Diagrams and Linear Correlation4.2 – Linear Regression and the Coefficient of Determinant

Focus Problem

“Changing Populations and Crime Rate”

• Read page 119-120 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 122-123– 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

Correlation Coefficient … r

Computation Formula

1. Compute – n = sample size

2. Compute r using formula

r =

• Careful: 2

Correlation Coefficient … r

1. Construct a scatter diagram2. From scatter diagram, do you think r will be pos, neg, or

zero? Why?3. Compute – n = sample size

4. Compute r using formula

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 coefficientρ = 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 120-131– Take notes on what we have not covered

• Do Problems – Page 131-136 (1-16)

• Check odds in back of book• Check all on website

• Read and preload 4.2 information– Notes/vocab