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| Graph that shows the relationship between two quantitative variables measured on the same individual |
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| When two variables experience increasing or decreasing associations simultaneously |
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| When two variables experience inversely related association; one increases while the other decreases |
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| Linear correlation coefficient (Pearson) |
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Definition
| A measure of the strength and direction of the linear relation between two quantitative variables |
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| Sample linear correlation coefficient, r = |
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Definition
Summation[(xi-xbar)/(sx)x(yi-ybar)/(sy)]/n-1
xbar = sample mean of explanatory variable
sx = sample sd of explanatory variable
ybar = sample mean of response variable
sy = sample sd of response variable |
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| 1. Properties of linear correlation coefficient |
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Definition
| Coefficeint is between -1 and 1; -1<=r<=1 |
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| 2. Properties of linear correlation coefficient |
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| If r = +1 then a perfect positive linear relation exists between the 2 variables |
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| 3. Properties of linear correlation coefficient |
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| If r = -1 then a perfect negative linear relation exists between the 2 variables |
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| 4. Properties of linear correlation coefficient |
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Definition
| The closer r is to +1, the stronger the evidence of positive association between the 2 variables |
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| 5. Properties of linear correlation coefficient |
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| The closer r is to -1, the stronger the evidence of negative association between the 2 variables |
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| 6. Properties of linear correlation coefficient |
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| If r is close to 0, then little or no evidence exists of a linear relation between the 2 variables |
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| 7. Properties of linear correlation coefficient |
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| The linear correlation coefficient is a unitless measure of association |
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| 8. Properties of linear correlation coefficient |
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Definition
| The correlation coefficient is not resistant |
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