Midterm 3

Wednesday, June 10, 1:10pm

Research Research ConceptsConcepts

Regression:Regression:Independent Independent

and Dependent and Dependent VariablesVariables

Regression

Instead of deciding whether the independent variable has "some effect" on your dependent variable, we wish to see how well we can predict the dependent variable (response variable) from the independent variable (explanatory variable).

Of course, if the independent variable has no effect on the dependent variable, then the independent variable will NOT help us predict the dependent variable.

If the independent variable has a strong effect on the dependent variable, then we will be very GOOD at predicting the dependent variable from the independent variable.

The RegressionModel

The RegressionModel

Linear(strong correlation) Linear

(weak correlation)

Linear(strong correlation)

Non-linear(strong correlation) Non-linear

(strong correlation)

Non-linear(no correlation) No Relationship

(no correlation)

The ‘Coefficient of Correlation’, r

How close are the datapoints in the scatterplot to the best-fitting

regression line?

The Coefficient of Correlation Statistic (r)

r is a value between -1 and 1.

r = 1: Perfect Positive Linear Correlation

r = -1: Perfect Negative Linear Correlation

r = 0: No Linear Correlation

What Do Correlations Tell Us?

Correlations allow us to predict one score from another (using the "regression equation").

Good prediction doesn't always require understanding why there is a relationship.

Correlation does not imply causation!

Correlations are often due to coincidences or common cause factors.

Correlation ≠ Causality

r = 0.98

Regression HypothesesRegression Hypotheses

• Null Hypothesis: Null Hypothesis:

HH00: : ββ11 = 0 = 0

• Alternative Hypothesis:Alternative Hypothesis:

HH11: : ββ11 ≠ 0 ≠ 0

Estimated Parameters

• From your data, we will get an estimate of β1.

• We will call this estimate B1.

• From your data, we will get an estimate of β0.

• We will call this estimate B0.

Estimated Parameters

• Slope

• Intercept

XBYB 10

formulanasty 1 B

(Do (Do notnot memorize this formula) memorize this formula)

Predicting Scores

B0 = B1 = Y =

If Mr. Bob's X score is what is his predicted score?

What is the deviation score?

Y =^

Y - Y =^

Intercept Slope

Regression

Answer me