Table of Contents
Correlation
Question: Is a chocolate cake’s price related to it quality
First the cakes are purchased and given a number from 1 to 10
The price of each cake is recorded and put away
An independent researcher will taste and evaluate each cake
The results of the taste test are recorded
It is not known which is the explanatory variable, just plot
The price and the quality are associated either way
The correlation coefficient gives the strength and direction
The correlation coefficient can be between plus and minus 1
A correlation greater than zero is called a positive correlation
A correlation less than zero is called a negative correlation
Correlation Calculation here is the calculation
Both the x and y are scaled by their standard deviation, S
The results are between +1 and -1 due to the average being taken
Correlation Coefficient
And the correlation is a positive 0.8
Let us look at twins raised together and twins raised apart
Twins, even twins raised apart have a lot in common
There have been studies on twins raised together and raised apart
Twins have a strong correlation in height, which is not surprising
There is also a correlation between personality traits, 0.49 raised apart, 0.52 raised together
Do these two graphs have a different correlation coefficient
The correlation is the same
Why is the correlation zero of this plot, are x & y not related
There is a positive correlation to this point then it is negative
Regression using x or y ?
Interpretation
Regression
Calculating Least-Square Regression line
take derivative to obtain values of m and b which minimize sum of square
Two Equations Two Unknowns
Here is the algebra
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Author: James M. Grow
Email: Grow@adm.njit.edu
Home Page: http://www-ec.njit.edu/~grow/statisti.htm
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