Test #3: Chapters 8-9

Correlation is the relationship between two variables whereby a

change in ONE VARIABLE is associated with a CONCURRENT change in the other

Correlation is measured

as to direction and the degree of association

Scatterplot is a graph with

plotted values for two variables that are being compared

This shows a

positive correlation

What is the concurrent change for positive correlation?

Same Direction

This shows

Negative Correlation

What is the concurrent change for negative correlation?

Opposite directions

This shows

Zero Correlation

-.92

(Look at the number rather than the sign)

What is r

Correlation Coefficient

Significance of r:

Computes

degrees of freedom = n - 2

Significance of r:
Critical value =

table R

Significance of r:
Computed r(df) >

Critical value

Correlation is NOT

causation

What is the coefficient of determination (r²) in statistics?

measures the part of the variance of one variable that can be explained by the variance of a related variable.

Why does the critical value of r increase as sample size decreases?

A correlation by chance is more likely

Linear regression

makes predictions based on linear relationships

Linear Regression:

The value of the correlation between _____

two variables adjusts the prediction

Linear Regression:

The higher the correlation,

the more accuracy

Regression Equation

Positive Correlation is also called

Direct Correlation

Negative Correlation is also called

Indirect Correlation

Correlations look at

straight line relationships

Degree of association is

how strong 2 things are related

Significance is related to

strength and consistency

What is this called

Directionality Problem or Third Variable Problem

n

number of PAIRS of scores

Level of Significance for One-Tailed Test

.05

95% certain

Level of Significance for One-Tailed Test

.01

99% certain

Significance of r

The computed r should be greater than

critical value

What are the regression coefficients?

b & a

(Y Hat)

Predicted value of Y

b

slope of regression line

b

the amount of change in _____________

Y associated with a 1-unit change in X

a

the y intercept of the regression line

a is the predicted value of _____________

Y when x = 0

X

the value of X used to predict Y

Regress means

to go back to

What is a?

Regression Line

Two different lines:

one to predict x and one to predict y

Standard Error of the Estimate

standard deviation we put around our prediction

Sign of standard error of estimate

What is b/slope

2.1

What is the y-intercept?

3.2

Coefficients:
+.83, +100, +10, -105, -90, -.85, +.08

Question:
Which of the following are valid correlation coefficients?

+.83, -.85, +.08

Coefficients:
+.83, +100, +10, -105, -90, -.85, +.08

Question:
Which is the largest?

-.85

Coefficients:
+.83, +100, +10, -105, -90, -.85, +.08

Question:
Which is the smallest?

+.08

What is the coefficient of determination?

r²

If tall people tend to marry tall people and short people tend to marry short people, would that be a positive or negative correlation?

positive correlation

Regression uses ___________ to __________

straight-line correlations; predict things

Regression does not guarantee that

you’re going to be right, it’s MOST LIKELY that you’re going to be right

If we don’t have any other information, our best guess goes back to the

mean/average