Upload
svea
View
29
Download
0
Tags:
Embed Size (px)
DESCRIPTION
4.2 Introduction to Correlation. Objective: By the end of this section, I will be able to… Calculate and interpret the value of the correlation coefficient. Correlation Equation. CORRELATION COEFFICIENT. Measures the strength and direction of a relationship between two variables - PowerPoint PPT Presentation
Citation preview
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.