[L8] Relationship between Variables Correlation and Regression

Question 1

We are interested in finding a way to represent ___
between scores. For example

Answer 1

association

Question 2

Types of Correlation

Answer 2

Bivariate; Multivariate Correlation

Question 3

Correlation does not prove __

Answer 3

Causality

Question 4

Multivariate Correlation have more ____ Validity

Answer 4

Ecological

Question 5

IGT & RMT = test of difference
Correlation = test of _
_

_

Answer 5

correlation/association

Question 6

___ – first and most obvious way to summarize
data where we are examining the relationship between
two variables

Answer 6

Scatterplot

Question 7

We put one variable on the x-axis and another on the yaxis,
and we ___for each person showing their
scores on the two variables.

Answer 7

draw a point

Question 8

test of correlation involved administering ___ tests in the same group of participants

Answer 8

2 or more different

Question 9

When we want to tell people about our results, we ____

Answer 9

don’t
have to draw a lot of scatterplots.

Question 10

__
_
_Children were asked to listen
to a word and repeat it. They were then asked which of
these 3 words started with the same sound.

Answer 10

Initial phoneme detection.

Question 11

____reading score, a standard
measure of reading ability.

Answer 11

British Ability Scale (BAS)

Question 12

We usually summarize and represent the relationship
between two variables with a ___
__
_
_

Answer 12

number (correlation
coefficient).

Question 13

We also calculate the ____ for this
number, and we want to be able to find out if the
relationship is ___

Answer 13

Confidence Intervals; statistically significant

Question 14

Thus, we want to know what is the probability of finding
a relationship at least this strong if the null hypothesis that
there is no relationship in the population is true.

Question 15

– a best fitting line
used for prediction

Answer 15

Line of best fit or Regression Line

Question 16

Predicting the variation in Y as a __
_

Answer 16

function of the variation
in X.

Question 17

– how steep the line
*

Answer 17

Slope

Question 18

___ – the position or height of the line.

Answer 18

Intercept

Question 19

By convention we give the height at the point where the
line ___

Answer 19

hits the y-axis.

Question 20

The
___ is called the y-intercept or often just the
intercept

Answer 20

height; (or sometimes the constant)

Question 21

The intercept represents the ___of a person
who scored _
_ on the x-axis variable.

Answer 21

expected score ; zero

Question 22

y=b0+b1X

Answer 22

regression expression, predicting behavior of y as function of x

useful for raw scores

Question 23

It is often the case that the intercept __. After all, __no one_usually scores ___

Answer 23

doesn’t make any
sense; 0 or close to 0.

Question 24

We can use the ___of slope and __ to
calculate the expected value of any person’s score on Y,
given their score on X.

Answer 24

two values, intercept

Question 25

y = β0 + β1x (sometimes it is y = a + bx or y = mx + c)
Where x is the x-axis variable. This equation is called the
___

Answer 25

regression equation.

Question 26

We can make a _
__ about one score from the
another score

Answer 26

prediction

Question 27

Problem: if we don’t understand the ___, regression
lines and equations are ___.

Answer 27

scale(s), meaningless

Question 28

thinking about the relationship between two variables can
be very useful

Answer 28

Making Sense of Regression Lines

Question 29

When there is a relationship between two variables, we
can ___ one from the other.

Answer 29

predict

Question 30

We can not say that one __ the other,

Answer 30

explains

Question 31

We need some way of making the scales have some sort
of meaning, and the way to do this is to
__ the data
into __

Answer 31

convert; standard deviation units.

Question 32

Talking in terms of SDs means that we are talking about
_
__

Answer 32

standardized scores.

Question 33

Because we are talking about standardized regression
slopes, we call it “___

Answer 33

standardized slope.

Question 34

___ – a more important name for the
standardized slope.

Answer 34

Correlation coefficient

Question 35

In order to convert the units, we need to know the ___

Answer 35

SD of
each of the measures.

Question 36

If we know the ___, we can calculate the correlation
using the formula: r = β x σx / σy

Answer 36

slope

Question 37

The letter r actually stands for ___, but most people
ignore that because it is confusing

Answer 37

regression

Question 38

Thus, if we know the _
__ we can calculate the correlation

Answer 38

slope

Question 39

3 ways to calculate for the correlation coefficient”r”

Answer 39

1. regression line
2. standardized slope
3. proportion of variance

Question 40

In correlation, we want to know how well the regression
line ___

Answer 40

fits the data.

Question 41

That is, how
___the points are from the line.

Answer 41

far away

Question 42

The __ the points are to the line, the stronger the
relationship between the two variables.

Answer 42

closer

Question 43

When we had one variable and we wanted to know the
spread of the points around the mean, we calculated the
_
_

Answer 43

SD (σ).

Question 44

The square of the SD is the _
__.

Answer 44

variance

Question 45

the difference between their
predicted score and their actual score. The difference is
called
_–.

Answer 45

Residual

Question 46

Their ____ (the difference between the score they
got and the score we thought they would get based on
their initial phoneme score)

Answer 46

residual score

Question 47

if we want to calculate the equivalent of the
variance, we need to ___ each person’s score

Answer 47

square

Question 48

___ = d squared

Answer 48

Residual squared

Question 49

The value of the standardized slope and the value of the
square root of the proportion of variance explained will
___ be the same value.

Answer 49

always

Question 50

We therefore have ___of thinking about
correlation.

Answer 50

two equivalent ways

Question 51

The first way is the ___
It is the expected
increase in one variable, when the other variable increases
by 1 SD.

Answer 51

standardized slope.

Question 52

The second way is the __
__ If you
square a correlation, you get the proportion of variance in
one variable that is explained by the other variable.

Answer 52

proportion of variance.

Question 53

A correlation is both ___statistics.

Answer 53

descriptive and inferential

Question 54

We can find the
____and we can also use
it to describe the ___

Answer 54

probability estimate ; strength of the relationship

Question 55

• __ – strength of relationship
  _

Answer 55

Magnitude

Question 56

___ – positive, negative, curvilinear etc.

Answer 56

Direction

Question 57

Cohen’s effect size:

Answer 57

• r = 0.1 = small correlation
• r = 0.3 = medium correlation
• r = 0.5 = large correlation

Question 58

Note that these only really apply in what Cohen, called
___

Answer 58

Social and Behavioral sciences.

Question 59

Common mistake

Answer 59

• A correlation around 0.5 is a large correlation.
• A correlation does not have to exceed 0.5 to be large.
• If you have a correlation of r = 0.45, you have a
  correlation which is approximately equal to a large
  correlation.
• It’s not a medium correlation just because it hasn’t quite
  reached 0.5

Question 60

Pearson Correlation Coefficient
* Also known as ___

Answer 60

Pearson Product moment correlation.

Question 61

Pearson Product moment correlation developed by

Answer 61

Karl Pearson

Question 62

Pearson Correlation Coefficient
is a _____ and makes the ___
made by other parametric tests.

Answer 62

Parametric correlation; same assumptions

Question 63

level of measurement for Pearson Correlation Coefficient

Answer 63

Continuous and normally distributed data

Question 64

to determine r

Answer 64

1. standardized slope
2. proportion of variance
3. pearson product moment correlation

Question 65

Optional Extra: Product Moments
* ___: the moment is the __ from the fulcrum
multiplied by the weight on the lever.

Answer 65

Physics; length

Question 66

___ the total moment is equal to the length
from the center, multiplied by the weight. The same principle applies with ___.

Answer 66

Seesaw analogy: correlation

Question 67

The same principle applies with correlation: needs to be balanced (raw to standard score) to be
_-
_

Answer 67

comparable

Question 68

• We find the _
  __ for each of the
  variables. In this case the center is the
  __.

Answer 68

length from the center; mean

Question 69

So, we calculate the difference between the score and the
mean for each variable (these are the ___) and then
we multiply them together (this is the ___).

Answer 69

moments; product

Question 70

Because this value is dependent on the ___
we need to divide it by N.

Answer 70

number of people,

Question 71

And because it is related to the ___, we
actually divide by N-1.

Answer 71

standard deviation

Question 72

This is called ___, and if we call the two variables
x and y,

Answer 72

covariance

Question 73

Just as before, we need to __ this value by
dividing by the ___

Answer 73

standardize; standard deviations.

Question 74

Calculating the Correlation
Coefficient:

we need to divide by ___, so we
multiply them together

Answer 74

both SDs

Question 75

Importance scattergraph or plot:
*

Answer 75

It will show us approximately what the correlation should
be.

It will help us detect any errors in our data, for example
data entry errors.

It will help us get a feel of our data.

Question 76

The confidence intervals for a statistic tell us the likely
___

Answer 76

range of a value in the population.

Question 77

Sampling distributions of correlation is ___. It is not __
_, which means we can’t add and
subtract CIs in the usual way.

Answer 77

tricky; symmetrical

Question 78

___transformation used which
makes the distribution symmetrical.

Answer 78

Fisher’s z transformation –

Question 79

Used to calculate the CIs and then transform back to
correlations.

Answer 79

Fisher’s z transformation –

Question 80

It is called a ____, because it makes the
distribution of the correlation into a z distribution which
is a normal distribution with a mean of 0 and SD of 1.

Answer 80

z transformation

Question 81

There are ___ to find the p-value associated with a
correlation.

Answer 81

2 ways

Question 82

Calculating the p-value

Answer 82

1. Use table in Appendix 3.

Question 83

If we really want to know the p-value, then we can
convert the value for r into a ___

Answer 83

value for t.

Question 84

We can use this t-value to obtain the __using
a __

Answer 84

exact p-value, computer program

Question 85

When we know the __ we can also calculate the
___ of the regression line

Answer 85

correlation; position

Question 86

We can use the two values ___ to create
a regression equation which will allow us to predict y
____ from x

Answer 86

(slope and intercept); (display behavior); (desirability).

Question 87

We can use the
___ to draw a graph with the line
of best fit on it

Answer 87

predictions

Question 88

we have extended the line to __ – we would not
normally do this.

Answer 88

zero