
Concept explainers
To Describe:
The strength, and the direction of the
Weak
Given:
The scatter plot of a data set:
Concepts Used:
When points on the scatter plot of a dataset are clustered along a straight line, then the data is said to have linear correlation.
The collective nearness of these points to a single straight line indicates the strength of linear correlation. This can be estimated by the width of an oval enclosing all the points tilted along the said straight line. The larger the width, the lesser is the strength of the linear correlation.
If the value of in the above estimated straight line increases with increasing values of
then the correlation is said to be positive in direction. If, on the other hand,
decreases with increase in
the direction of correlation is said to be negative. In terms of an oval drawn around the points, if the oval is tilted along a line with a positive slope, then the correlation is positive, and if the oval is tilted along a line with negative slope, then the correlation is negative.
Calculations:
Draw an oval enclosing the points on the data.
Interpretation:
The oval enclosing the points is tilted along a straight line, indicating linear correlation.
The oval’s width as about half of its length. Thus, the strength of correlation is weak.
The oval is tilted along a line with positive slope, thus the direction of linear correlation is positive.
Conclusion:
The given scatter plot represent a data set with weak positive linear correlation.
Chapter 2 Solutions
EBK PRECALCULUS:GRAPHICAL,...-NASTA ED.
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