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Response Variable

The variable whose value can be explained by the value of the explanatory or predictor value

 

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Scatter Diagram

a graph that shows the relationship between two quantitative variables measured on the same individual. Each individual in the data set is represented by a point in the scatter diagram. The explanatory varaible is plotted on the horizontal axis, and the response variable is plotted on the vertical axis. 

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Positively Associated

two variables that are linearly related are positively associated when above-average values of one variable are associated with above-average values of the other varaible and below-average values of one variable are associated with below-average values of the other variable. Two variables are positively associated ifm whenever the value of one variable increases, the value of the other variable also increases, 

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Negatively Associated

Two variables that are linearly related are negatively associated when above-average values of one variable are associated with below-average values of the other variable. That is, two variables are nergatively associated if, whenever the value of one variable increases, the value of the other variable decreases. 

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Linear Correlation Coefficient (Pearson product moment correlation coefficient)

is a measure of the strength and direction of the linear relation between two quantitative variables. The Greek letter p(rho) represents the population correlation coefficient, and r represents the sample correlation coeffictient. 

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Properties of Linear Correlation Coefficient

1. The linear correlation coefficient is always between -1 and 1, inclusive.

2. IF r=+1, then a perfect positive linear relation exists between the two variables

3. If r=-1 then a perfect negative linear relation exists between the two variable

4. The close r is to +1 the stronger is the evidence of positive association between the two variables

5. the closer r is to -1 the stronger is the evidence of negative association between the two variables

6. If r is close to 0, then little or no evidence exists of a linear relation between the two variables. So r close to 0 does not imply no relation, just no linear relation

7. The linear correlation coefficient is a unitless measure of association. So the unit of measure for x and y plays no role in the interpretation of r.

8. Tge correlation coefficient is not resistant. Therefore, an observation that not follow the overall pattern of the data could affect the value of the linear correlation coefficient. 

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Testing for a Linear Relation

1. Determine the absolute value of the correlation coeffecient

2. Find the critical value in Table II from Appendix A for the given sample size

3. If the absolute value of the correlation coefficient is greater than the critical value, we say a linear relation exists between the two variables. Otherwise no linear realtion exists.