4.2 introduction to correlation

4.2 Introduction to Correlation

Objective:By the end of this section, I will beable to…

• Calculate and interpret the value of the correlation coefficient.

Correlation Equation

2 22 2

/

/ /

xy x y nr

x x n y y n

CORRELATION COEFFICIENT

Measures the strength and direction of a relationship between two variables

Is denoted by the letter rThe range is from -1 to +1

EXAMPLES r = + 1 r = + 0.75 r = + 0.5 r = +0.25 r = 0 r = - 0.25 r = - 0.5 r = - 0.75 r = - 1

STRONG +Slightly strong +Moderate +Weak +

No Association

Weak -Moderate -

Slightly Strong -STRONG -

EXAMPLES

r = + 1r = + 0.7r = - 0.5r = 0r = + 0.3r = - 1

Strong PositiveAssociationSlightly StrongPositiveAssociation

ModerateNegativeAssociation

No AssociationWeakPositiveAssociation

StrongNegativeAssociation

4.3 Introduction to Regression

Objectives:By the end of this section, I will beable to…

1) Calculate the value and understand the meaning of the slope and the y intercept of the regression line.

2) Predict values of y for given values of x.

Algebra Days

Remember the formula:y = mx + by and x are the variablesm is the slope of the lineb is the y-intercept

Algebra Days

Then – linear equationNOW – linear regression

NEW SYMBOLS

y and x are the variablesm = b1 is the slope

b = bo = a is the y-intercept

Using data to predict the future

Once we have graphed the data and determined the association, we can fit a regression line which best fits or models the data.

Line of Best Fit

Select DiagnosticOn from Catalog to get r2 and r values with LinReg.

For LinReg ALWAYS use Choice #8 NOT #4.

http://www.keymath.com/documents/sia2/CalculatorNotes_Ch03_SIA2.pdf

LINE OF BEST FIT

REGRESSION LINE

Regression Lines

The Regression Line is sensitive to Outliers.

Actual vs. Predicted Values

ExampleIn BMX dirt-bike racing, jumping high or

“getting air” depends on many factors: the rider’s skill, the angle of the jump, and the weight of the bike. Here are data about the maximum height for various bike weights.