Transcript LinReg

Run the colour experiment
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yellow …first
Linear Regression
• In probability theory and statistics,
correlation (often measured as a
correlation coefficient) indicates
the strength and direction of a
linear relationship between two
random variables.
A scatterplot allows
you to search for
Trends
Strong Positive Correlation:
- strong trend, LOB has a
positive slope
Weak Positive Correlation
- not a strong trend, LOB
has a positive slope
Negative Correlation:
- The LOB has a negative
slope.
A correlation coefficient is a
number between -1 and +1
which measures the degree
to which two variables are
linearly related.
The closer the value is to 1.0, the
stronger the relationship.
The closer the value is to 0.0, the
weaker the relationship.
Positive and negative just define
slope.
For Pearson’s product-moment
correlation coefficient, the greek
letter rho (r) is used.
0.80-1.00 Strong Association between
Variables
0.60-0.79 Strong-Moderate Association
0.40-0.59 Weak-Moderate Association
0.30-0.39 Strong-Weak Association
0.20-0.29 Weak-Weak Association
0.00-0.19 Little, if any association
If there is perfect linear relationship
with positive slope between the two
variables, r = 1
If there is a perfect linear
relationship with negative slope
between the two variables, r = -1.
If r = 0, there is no linear
relationship between the variables.
Coefficient of Determination
r2 represents the fraction of
variability in y that can be explained
by the variability in x.
For example, if r2 = 0.44, this means
that 44% of the variation of the
dependant variable is due to the
variation in the independent variable.
homework
• Pg 168 1,2,3,5,6
• Pg 180 6