HOME WORK WEB PAGE FOR CLASS MATH 251 & MATE 251 & MATE 345

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Chapter 3 Descriptive Statistics

 

3.5 Measures of Relation Between Two Variables

 

In this section we present covariance and correlation as descriptive measures of the relationship between two variables.

 

            Covariance

           

For a sample of size n with the observations (,), (,) and so on, the sample covariance is defined as follows:

 

Sample Covariance

 

            s=

 

This formula pairs each   with a

 

Correlation Coefficient

r=

                                   r=Sample correlation Coefficient

                                   = Sample Covariance

                                   = Sample Standard Deviation for x

                                   =Sample Standard Deviation for y

                                  

Home Work

1.      Compute the sample correlation coefficient for PCs file

2.      What does the sample PCs correlation coefficient tell about the relationship between the performance score and overall rating?

3.      Compute the sample correlation coefficient for DowS&P file. Are they poorly correlated, or do they have a close association?

4.      What is the correlation between the high and low temperature for the file HighLow

5.       

Driving Speed

30  50  40  55  30  25  60  25  50  55

KM

28  25  25  23  30  32  21  35  26  25

                                  

a.      KM in Horizontal Axis, Develop a scatter diagram and interpret it

b.      Compute and interpret covariance

c.      Compute the sample correlation coefficient for the data.

d.      What does this value tell us about the relationship between two variables?