PRED 354 TEACH. PROBILITY

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PRED 354 TEACH. PROBILITY STATIS. FOR PRIMARY
MATH

• Lesson 14
• Correlation Regression 

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Correlation
It is a statistical method that is used to
measure and describe a relationship between two
variables. Two variables are observed. No
attempt to control or manipulate the variables.
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Correlation

• Its characteristics
• The direction of relationship
• 1. Positive correlation (Two variables tend to
  move in the same direction) ()
• 2. Negative correlation (Two variables tend to
  move in the opposite direction) (-)

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Correlation
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Amount of coffee sold
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Temperature
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Correlation

• Its characteristics
• b. The form of the relationship
• The relationship tend to have a linear form.
  (parabolic, in other words not a straight-line
  relationship)
• The degree of the relationship
• A correlation measures how well the data fit the
  specific form being considered.
• A perfect correlation 1
• No fit 0

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Correlation
Where and why correlations are used 1.
Prediction If two variables are known to be
related in some systematic way, it possible to
use one of the variables to make accurate
predictions about the other. EX 2. Validity
Suppose that you develop a new test for a
specific purpose. How could you show that this
test truly is measuring what it claims? EX
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Correlation
Where and why correlations are used 3.
Reliability A measurement procedure is
considered reliable to the extent that it
produces stable consistent measurement. EX 4.
Theory Verification Many theories make some
specific prediction about the relationship
between two variables EX
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Correlation
The Pearson Correlation (Interval o ratio scale)
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Pearson Correlation
NEW The sum of products of deviations (SP) for
measuring the amount of covariability between two
variables.
SSto measure the amount variability for a single
variable
SP a parallel procedure for measuring the amount
covariability between two variables
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Pearson Correlation
X Y
0 1
10 3
4 1
8 2
8 3
EX
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Pearson Correlation Interpretations

1. It describes a relationship between two
   variables. It does not explain why the two
   variables are related. (Not proof of a
   cause-and-effect relationship between two
   variables) (EX )
2. The value of correlation can be affected by the
   range of scores. (EX)
3. One of two extreme points (outriders) can have
   dramatic effect on the value of a correlation
   (EX)
4. How good? There is no proportion(Coefficient of
   determination)

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Coefficient of determination
The value of r2 is called by coefficient of
determination because it measures the proportion
of variability in one variable that can be
determined from the relationship with other
variables. EX r .80 and r2 .64. It means
that 64 of the variability in the Y scores can
be predicted from the relationship with X.
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Hypothesis testing
H0 ? 0 (There is no correlation). df
n-2 Table B.6 (independent of sign) To be
significant, the magnitude of the sample
correlation must equal or exceed the value in the
table. EX A researcher obtains a correlation of
r -.41 for a sample of n25 individuals. Does
this sample provide sufficient evidence to
conclude there is significant, non-zero
correlation in the population?
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Regression Equation
The regression equation for Y is the linear
equation Where the constants b and a are
determined by
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.
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Amount of beer sold
Regresson line
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Temparature
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Regression line

1. It makes relationship easier to see.
2. It identifies the center or central tendency of
   the relationship.
3. It can be used for prediction

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Example
EX The following table presents students
anxiety rating (15 minutes before the exam) and
exam scores. a. Compute the correlation
between AR and ES. b. Is the sample correlation
significant at the .05 level? c. Find the
regression line equation d. Predict a students
reaction time whose AR score is 10.
Student Anxiety rating Exam Score
A 5 80
B 2 88
C 7 80
D 7 79
E 4 86
F 5 85