Correlation And Regression

Front 1

Two of the most powerful and versatile approaches for investigating variable relationships

Back 1

correlation analysis
regression analysis

Front 2

shows the relationship between two quantitative variables measured on the same individuals

Back 2

scatterplots

Front 3

scatter plot displays (3) of the relationship

Back 3

form (linear or nonlinear)
direction (+ or -)
strength (no, weak, or strong)

Front 4

relationship examined by our eyes may not be satisfactory in many cases we need numerical measurement to supplement graph
____is the measure we use

Back 4

correlation

Front 5

The correlation measures the

Back 5

direction and strength of the linear relationship between two quantitative variables
*Pearson correlation coefficient (r)

Front 6

Pearson correlation coefficient is
standardized ______

Back 6

covariance

Front 7

Covariance=

Back 7

degree to which X and Y vary together

Front 8

Cov(X,Y) > 0 means

Back 8

X and Y tend to move in the same direction

Front 9

Cov(X,Y) < 0 means

Back 9

X and Y tend to move in opposite directions

Front 10

Cov(X,Y) = 0 means

Back 10

X and Y are independent

Front 11

explain -1 ≤ r ≤ +1

Back 11

-closer to –1, the stronger the negative linear relationship
-the closer to 1, the stronger the positive linear
relationship
-the closer to 0, the weaker any linear relationship

Front 12

T or F correlation is It is an indicator of causal relationship between variables

Back 12

F
its NOT

Front 13

only legitimate way to try to establish a causal connection statistically is

Back 13

through the use of designed experiments

Front 14

what Statistical test can be used for the significance
of correlation coefficient if a single parameter

Back 14

t test
*we can use the original and convert it for correlation coefficient

Front 15

linear regression:
Correlation treats two variables X and Y as_____
(it shows a ____relationship)

Back 15

equal
symmetric linear

Front 16

In many cases, we want to study a ______linear relationship between X and Y.
meaning?

Back 16

-asymmetric
-One variable (X) influences (or predicts) the
other variable (Y).
X = IV or predictor variable
Y = DV or outcome variable

Front 17

Linear Regression Analysis=

Back 17

Describes how the DV (Y) changes as a single independent variable (X) changes (the effect of X on Y)
*called ‘simple’ linear regression analysis
**summarizes the relationship between two variables if the form of the relationship is linear

Front 18

linear regression model is used as a

Back 18

mathematical model to predict the value of DV (Y) based on a value of an IV (X)

Front 19

When a scatterplot displays a linear pattern, we can describe the overall pattern by

Back 19

drawing a straight line through the points.

Front 20

The equation of a line fitted to data gives a
compact description of the dependency of the___on the___

Back 20

DV on the IV
*equation of a line is a mathematical model for the straight-line relationship

Front 21

What is the “equation of line”?

Back 21

A straight line relating Y to X has an equation of the
form:
Ŷ = a + bx
a = intercept (Mean value of DV when IV is zero)
b= slope (Amount by which DV changes on average when IV changes by one unit)

Front 22

simple regression model

Back 22

fits a straight line through the set of n points in such a way that makes the sum of squared residuals of the model (that is, vertical distances between the points of the data set and the fitted line) as small as possible.

Front 23

simple regression (II)

Back 23

..

Front 24

When we have a scatterplot with a linear relationship between the DV (Y) and a single IV (X), we are often interested in summarizing the overall pattern
this is done how

Back 24

drawing a line on the graph=regression line.

Front 25

regression line =

Back 25

straight line that describes how Y changes as X changes.

Front 26

How to determine the best regression line?

Back 26

-line that comes the closest to the data points in the
vertical direction. There are many ways to make this distance “as small as possible.”
-use method of least squares

Front 27

least-squares regression line of Y on X is the line that

Back 27

makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

Front 28

Sum of the Squares of all vertical distances=

Back 28

SS (ERROR)

Front 29

in the least squares method which is determined/calc first a or b

Back 29

b then a

Front 30

-can we use statisitcal tests to test the strength of the
relationship between the two variables in simple linear regression (the effect of X on Y)
-if so what are the hypothesis

Back 30

-yes
-H0 : β = 0 (β = population slope)
There is no linear relationship between X and Y
(no effect of X on Y)
H1 : β ≠ 0
There is a linear relationship (an effect of X on Y)

Front 31

Statistical test for the significance of slope

Back 31

-just use/edit the t statistic
-If the observed value of t is greater than a critical value of t with DF = N-2 and α = .05, we may reject the null hypothesis

Front 32

to apply the t test for the slope, the following assumptions are required (2)

Back 32

Normal distributions
Independent observations

Front 33

As in ANOVA, we can also divide the variance/variation in the DV (Y) into different parts resulting from different sources
-In regression analysis, the total variation in Y is partitioned into(2)

Back 33

SS(Regression): The variation in Y explained by the regression line
SS(Error): The variation in Y unexplained by the regression line (residuals).

Front 34

simple regression:
the_____is used for testing

Back 34

F statistic
Ho : β = 0
H1 : β ≠ 0
If the observed F value is greater than a critical value of F with DF(Reg) and DF(E) at α= .05, we may reject H0.

Front 35

Coefficient of Determination (R^2)=
used to
range

Back 35

-SS(regression)/SS(T)
*Proportion of the total variation in Y accounted for by the regression model.
-assess goodness-of-fit of the regression model
-0-1

Front 36

The larger R^2, the more ____of DV explained
0 =
1=

Back 36

variance
No explanation at all
Perfect explanation.

Front 37

in simple regression, r=

Back 37

√R^2

Front 38

example:
r^2=.710 means what

Back 38

71% of the total variance of the DV is explained by the IV

Front 39

Note that in simple regression analysis, both____(2)
tests are used for testing the significance of the single
slope, resulting in the same conclusion.

Back 39

F and t