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Ch 4- Scatter Diagrams and Correlation
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Terms in this set (16)
Response (dependent) Variable
the variable whose value can be explained by the value of the explanatory or predictor variable
Explanatory Variable (independent) & Response Variable plotted on
Explanatory- X-Axis (basis)
Response- Y-Axis (outcomes)
Interpreting Scatter Graphs
Bivariate Data
Data with two variables measured on an individual
Scatter Diagram (+ types)
a graph that shows the relationship between two quantitative variables measured on the same individual
Linear
Nonlinear
No relation
Linear Correlation Coefficient
a measure of the strength and direction of the linear relation between two quantitative variables
(rho) = population correlation coefficient
r = sample correlation coefficien
Properties of the Linear Correlation Coefficient
A) The linear correlation coefficient is always between:
-1 and 1
-1 <_ r <_ 1 inclusive
B) if r = +1
A perfect positive linear relation exists between the two variables
C) if r = -1
A perfect negative linear relation exists between the two variables
D) the closer r is to +1
The stronger is the evidence of positive association between the two variables
E) the closer r is to -1
The stronger is the evidence of negative association between the two variables
F) if r is close to 0
Little or no evidence exists of a linear relation between the two variables
R close to 0 does not imply no relation, just no linear relation
G) linear correlation coefficient is a unitless measurement of association
Unit of measure for x and y plays no role in the interpretation of r
H) the correlation coefficient is not resistant
Therefore, an observation that does not follow the overall pattern of the data could affect the value of the linear correlation coefficient
How do I know the correlation between two variables is strong enough for me to conclude that a linear relation exists between them? (3 steps)
Test for linear relation
Step 1: determine absolute value of the correlation coefficient
| r |
Step 2: find the critical value in table 2 for given sample size
Step 3: if the absolute value of the correlation coefficient is greater than the critical value we say a linear relation exists. Otherwise no linear relation exists.
| r | > critical value
Why should numerical summaries of bivariate data be used in addition to graphs to determine any relation that exists between two variables?
Because we can manipulate the scale of graphs of bivariate data, possibly resulting in incorrect conclusions.
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