Statistics Chapter 8
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There are two variables that are being plotted as one dot on the X and Y
Variables can be either independent or a dependent of the other variable. For instance weight can be independent of a person's height.
Independent variable is thought to influence dependent variables.
When there is a strong between two variables then knowing one helps a lot in predicting the other. If the association is weak then knowing one variable won't help guessing the other.
The closure two variable are to the 45 degree line the stronger the association.
Sloping of The cluster
If the cluster is sloping upward it has a positive Correlation
If it Slopes downward it is a has a negative Correlation
Point of Average and SD
The point of average locates the center of the cluster.
Most points will be within 2 SD of the Cluster of both the Y and X axis
- X= Horizontal Cluster
- Y= Vertical Cluster
Correlation Coefficient Clustering
Correlation near 1 means Tight Clustering (r=1)
Correlation near 0 means Loose Clustering (r=0)
Corelation coefficient = r
- The measure of Linear Association or Clustering around a Line. (SD Line)
- It can be summarized by
The average of the x-values, The SD of x-value
The average of the -values, The SD of y-values
The correlation coefficient r
The closer r is to 1 the stronger the linear association between the variables and the more tightly cluster are the points around a line.
The LINE is the correlations of all the plotted points.
A prefect correlation is where r = exactly 1 (example y=x). It is said to have a correlation of r=1.
Correlations are always 1 or less.
Warning r=.80 does not mean 80%
Correlation of r=.9-1 is more of a line shape.
Correlation of r=.5 is more of a cloud looking shape
Correlation of r=0 is scattered and has no form or predictability
Correlations are always between r=-1 and +1
Points in a scatter diagram generally seem to cluster around the SD line.
1. The SD line goes through the point of averages.
2. It goes through all points which are an equal number of SD away from the the average for Both Variables (X and Y)
3. A person who has SD of 1 on both the Y and X points will be plotted of the SD line. However, if the X or Y value is not whole number away (1,2,3,4,) they will not be plotted on the line. (Example X= 2.5 SD and Y=2) will not be plotted on the SD line.
Computing the Correlation Coefficient
R=average of (X in Standard Units) multiplied by (y in Standard Units).
X plots = 1,2,3,4,5,6,7
Find average x
Find SD of x
(do this for each x value... not all together)
- 3. Subtract the average from x Values;and divide it by the SD for each x values.
Note: this will give you the values in standard units. (Example -1.5, .75, 1.75, etc)
Do the same thing for y values
multiply the values of each y and x corresponding values
(the values that were converted to standard units)
- (x in standard units) X (y in standard units).
last take the average of the multiplied values (the product)
.5 + 1 - .75 + 2 - 1 + .75 +1
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