Exam 3

Regression line

Allows us to make predictions 1) Extent of the variability around the regression line

The Pearson r might be thought of as a proportion, that when multiplied by 100, yields the percent of variance, on one variable explained by the other.

False

The maximum value of a Pearson r is 0.00.

False

The purpose of a Pearson r is to establish the central tendency of a set of scores.

False

2

The response variable (DV) is the direct cause of the exlamptory variable (IV) ex. social status & health or self esteem & academic achievements x -----> y x <-----y

3) Point where the line crosses he y-axis (y-intercept)

y' = mx+b

Problems w/ correlations

3 problems

Some reasons two variable may be related

7 reasons

6

Both variables are changing over time

5

Both variables may result from a common cause (third variable) x & y <---- z

4

Cofounding variables may exist

Correlations

Establish the degree of the relationship

A Pearson r of -0.97 represents a very weak relationship.

False

A Pearson r of 1.00 represents no relationship.

False

All negative relationships are weak.

False

For a Pearson r of -0.36, the coefficient of determination equals -0.06.

False

For a Pearson r of -0.40, 40% of the variance on one variable is explained by the other.

False

For a Pearson r of -0.62, a majority of the variance on one variable is explained on the other.

False

For a Pearson r of 0.75, 75% of the variance on the one variable is explained by (accounted for) the other.

False

If a Pearson r between two variables is very strong, this provides clear evidence that one variable affects the other.

False

If a relationship is extremely strong, a Pearson r will have a greater value than 1.00.

False

What do scatter plots tell us?

If the relationship between two interval or ratio variables is linear or not

Pearsons Correlation Coefficient (r)

Number between -1 and 1 that describes the linear relationship between pairs of measurement variables 1) Sign of r ( + or - ) indicates type of relationship 2) Value of r, without regard to the sign, indicates the strength of the relationship

Simple linear regression

One variable to make the prediction ex. ACT to predict college GPA

Regression

Procedure for making predictions about one variable based on its relation with another variable

2) Slope of the line (ties in w regression line)

Rise over run angle or tilt of the line; positive or negative

Least squares criterion

States that the variability around the line will be at a minimum ∑(y-y') = minimum If there was a zero, it would mean it's on the line

What do correlations measure

Strength and direction between two interval or ratio variables

Perfect linear relationship

Strongest relationship you can have with two variables r = 1

7

The association may be nothing more than a coincidence

3

The exlamptory variable (IV) is contributing but sole because of the response variable (DV)

1

The exlamptory variable (IV) is the direct cause of the response variable (DV)

Coefficient of determination (r^2)

The proportion of variability in the y-variable that is accounted for by the x-variable "variability accounted for" = R^2

A Pearson r indicates both the strength and direction of a relationship.

True

A Pearson r is a type of correlation coefficient.

True

A Pearson r of -0.50 is more likely to be called "moderately strong" than to be called "weak."

True

A Pearson r of 0.50 is more likely to be called "moderately strong" than to be called "weak."

True

A Pearson r of 0.95 represents a very strong relationship.

True

A scatter diagram with dots that form a patter going from the lower left have corner to the upper right hand corner represents scores that would yield a positive value of r.

True

A simple correlational study is usually NOT suitable for identifying cause-and-effect relationships.

True

For a Pearson r of -.60, the coefficient of determination equals 0.36.

True

For a Pearson r of -0.22, about 95% of the variance on one variable is NOT explained by the other.

True

For a Pearson r of 0.50, the coefficient of determination equals 0.25.

True

For a Pearson r of 0.80, 36% of the variance on one variable is explained by the other.

True

For a Pearson r of 0.90, 81% of the variance on one variable is explained by the other.

True

For making predictions from one variable to another, a Pearson r of -0.78 is better than a Pearson r of 0.52.

True

The possible values of a Pearson r is -1.00 to 1.00.

True

The square of Pearson r is called the coefficient of determination.

True

Multiple regression

Use several variable to make the prediction

Criterion Variable

Variable being predicted ex. Your GPA, a successful team we always predict the y-variable (y')

No relationship

Weakest relationship r = 0

Groups combined inappropriately may mask relationship (w regression line)

ex. height and weight with both male and female correlation does not imply causation