Chapter 6- Correlation and Regression

Question 1

What is a univariate distribution?

Answer 1

It is a frequency distribution where you’re only working with one variable
Ex. height, time, test scores, errors

Question 2

What is a bivariate distribution?

Answer 2

A frequency distribution where the scores on the two variables are paired
Bivariate distributions are required in order to use correlation and regression techniques
They also may show positive/negative/zero correlation

Question 3

What is considered to be a positive correlation and give an example?

Answer 3

It’s when high measurements on one variable tend to lead to high measurements on the other variable.
And low measurements on one variable also tend to lead to low measurements on the other variable.
Example- all fathers tend to have sons who grow up to have sons who grow up to be tall men, and
short fathers tend to have sons who grow up to be short men

Question 4

What is considered to be perfect correlation?

Answer 4

When the coefficient of correlation, r, is equal to 1.00
When there is perfect correlation all points fall exactly on the regression line
The only requirement for perfect correlation is that the differences between the pairs all be the same

Question 5

What is a regression line also referred to as?

Answer 5

The line of best fit

Question 6

What is a scatterplot?

Answer 6

It is a graph of the scores of a bivariate frequency distribution

Question 7

What do you see graphically in a scatterplot with negative correlation?

Answer 7

Increases in one variable are accompanied by decreases in the other variable (they have an inverse relationship).
The line of regression goes from the upper left corner of the graph to the lower right corner, it has a negative slope

Question 8

Is there a such thing as a perfect negative correlation?

Answer 8

Yes, when r = -1.00

Question 9

What is r and what does it tell us?

Answer 9

r is the correlational coefficient
It gives us the degree of relationship of two variables. One value on a plot isn’t more valuable than the other.
We just want to find how correlated the two factors are to find out how they relate.
And you’d rather have a stronger r value towards 1 or -1, because it helps solidify your data rather than a small
correlation

Question 10

Examples of negative correlation

Answer 10

Daily rain and daily sunshine, grouchiness and friendships, highway driving speed and gas mileage

Question 11

What does having zero correlation mean?

Answer 11

That the high and low scores on the two variables are not associated in any predictable manner
There is no linear relationship between the two variables
When r = 0.00 the regression line is literally just a horizontal straight line

Question 12

What are the two computational formulas used to find r?

Answer 12

The blanched formula and the raw-score formula
We’re going to be using the blanched formula, because it uses means and standard deviations to find it (bro, but
I really like just using the raw-score formula

Question 13

What is N when concerned with the computational formulas?

Answer 13

It isn’t every single data set or point. It is the number of number PAIRS.

Question 14

What is r used for sample or population?

Answer 14

r is used for a sample statistic. The population parameter is symbolized by the Greek letter rho (weird p, in physics it’s
for density or pressure or somethin’)

Question 15

What is considered small, medium, and large for the correlational coefficient?

Answer 15

Small- 0.10
Medium- 0.30
Large- 0.50

Question 16

What is the coefficient of determination?

Answer 16

It is literally r squared.

It is an estimate of common variance.

Question 17

How can you help determine r in a scatterplot?

Answer 17

If you draw a circle/envelope around the scatterplot. It helps the picture become clearer.

Question 18

How does an envelope around a scatterplot indicate low/high correlation?

Answer 18

The thinner the envelope, the larger the correlation. Because the points are closer to the line of regression.
The larger the envelope, the smaller the correlation.

Question 19

What does the coefficient of determination tell you and how does it differ from r?

Answer 19

r squared is different because. Okay. You get r. It tells you the proportion of variance among the data, right? Well.
You square it for r squared. This is the amount of common variance. And then you get a number. Let’s say you get 0.42.
Subtract this from 1, and you get 0.58 left right?This is the independent variance. This means that 58% of the variance
is due to other factors.

Question 20

What is independent variance?

Answer 20

It’s the r squared subtracted from 1.0. It is the variance that is due to other factors. Variance in one test that is not
associated with variance in the other test

Question 21

With a ven diagram how can we interpret where the common and independent variances lie?

Answer 21

Common variances are in the middle. Factors that influence both variables.
Independent variances are on the outside. On each variables side. These are the factors that ONLY influence the variable
that they are associated with

Question 22

How does the coefficient of variance test reliability?

Answer 22

We are able to test the reliability of the experiment of itself. I’m talking about its measuring devices specifically.
Devices such as tests, questionnaires, and/or different testing instruments.
If the devices are reliable they will produce consistent scores that are not subject to change fluctations.
What I mean by this is that if you test it once and get a score, and then test it twice and get a score,
r would still be relatively the same.

Question 23

What is considered a reliable r value for social science measurements?

Answer 23

An r of 0.8 or higher indicates reliability

Question 24

What is the golden rule concerning correlation/causation?

Answer 24

Correlation does NOT equal causation.
There are so many other factors that could’ve been related.
Example- researchers concluded smoking killed people. And although this was true, they concluded too early, because
the people who smoke tended to also be heavily stressed which caused them to smoke in the first place. It is important
to have well formed control groups to prevent these other confounding variables.

Question 25

What does r look like with a curved regression line?

Answer 25

If a curved regression line fits the data better than a straight line, r will be low, not reflecting the true
relationship between the two variables.
That’s why it may be important to look at a scatterplot to determine if the Pearson r value is appropriate for
the data set at hand.

Question 26

What is a truncated range?

Answer 26

when the range of the sample is smaller than the range of the population

Question 27

What is a linear regression line and what can you use it to do?

Answer 27

Linear regression is a technique that uses the data to produce an equation for a straight line.
You can use it to make predictions.

Question 28

What is the regression equation?

Answer 28

It is literally the slope intercept equation. But with a and b.