MMW W9 •Regression •Correlation

Linear regression

is the simplest and commonly used statistical measure for

prediction studies.

Linear regression

1. independent or predictor variables

2. dependent or criterion

It is concerned with finding an equation that uses the known values of one or more variables, called the 1. ___ , to estimate the

unknown value of quantitative variable called the 2. ___

It is a prediction when a variable (y) is dependent on the second variable (x)

based on the regression equation of a given set of data.

After a scatter plot is constructed and the value of correlation coefficient 1s

deemed to be significant, then an equation of the regression line 1s

determined.

The regression line is the data's line to be fit.

The closer the points fit the regression line, the higher the absolute value of r

s and the closer it will be to + 1 or to -1.

When b > 0, y

increases as x increases. In this case,

we say that y is directly or positively related to x.

CHARACTERISTICS OF THE REGRESSION LINE

Positive Linear Relationship

When b > O, y increases as x increases. In this case,

we say that y is directly or positively related to x.

Negative Linear Relationship

When b < O, y decreases as x increases. In this case,

we say that y is inversely or negatively related to x.

No Relationship

When b = 0, y is constant and is equal to y-intercept a. This

implies that there is no change in Y whatever X value is.

 scatter plot

is a graph of ordered pair (x, y) of numbers consisting of the

independent variable x, and the dependent variable, y.

Independent variable

is the variable that can be controlled or manipulated.

dependent variable

is the variable that cannot be controlled or

manipulated.

1. independent

2. dependent

The 1. ___ variable is plotted on the horizontal axis and the 2. ___

variable on the vertical axis.

positive linear, negative linear, curvilinear, or no discernible relationship.

The purpose of this graph is to determine the nature of the relationship

between the variables. The relationship may be ____

Correlation

is a statistical method used to determine if there is a relationship

between variables and the strength of the relationship.

Pearson Correlation Coefficient

The degree of linear association/relationship between two variables (at least of

interval scale) is measured by a correlation coefficient, denoted by r.

+1.0 Perfect (Positive/Negative) Correlation

+0.80-0.99 Very Strong (Positive/Negative) Correlation

+0.60-0.79 Strong (Positive/Negative) Correlation

+0.40-0.59 Moderate (Positive/Negative) Correlation

+0.20-0.39 Weak (Positive/Negative) Correlation

+0.01- 0.19 Very Weak (Positive/Negative) Correlation

0.0 No Correlation

Pearson Correlation Coefficient Interpretation