Term
| Associations between Variables |
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Definition
• Positively associated if increased values of
one variable tend to occur with increased
values of the other
• Negatively associated if increased values of
one variable occur with decreased values of
the other |
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Term
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Definition
A response variable (Y-axis) measures an
outcome of interest. Also called dependent |
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Term
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Definition
An explanatory variable (X-axis) explains
changes in response. Also called independent
• Explanatory does not mean causal: there are
often several possible explanatory variables
• Example: Study of heart disease & smoking
• Response: death due to heart disease
• Explanatory: number of cigarettes smoked per day
• Example: City dataset
• Response: mortality
• Explanatory: education |
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Term
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Definition
Some associations are not just positive or
negative, but also appear to be linear
A perfect linear relationship is Y = a + bX |
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Term
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Definition
| Can examine relationships of categorical variables this way. |
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Term
| Describing/ Examining a Scatterplot |
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Definition
Look for the overall pattern and for striking deviations from that patter.
You can describe the overall pattern of a scatterplot by the form, direction, and strength of the relationship.
An important kind of deviation is an outlier |
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Term
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Definition
measures the direction and strength of the linear relationship between two quantitatie variables. Correlation is usually written as r.
r is positive when there is a positive association
correlation makes no use of the disticntion between explanatory and response variables. Doesn't make a difference which variable you call x and which you call y in calculating the correlation.
requires that both variables be quantitative* key difference between correlation and association, because association can apply to categorical
always a number between -1 and 1. values near 0 indicate very weak linear relationships. Extreme values of -1 and 1 only occur when the points in a scatterlot lie exactly along a straight line.
correlation can ONLY apply to linear relationships (a curved relationship, no matter how strong, cannot be described by a correlation)
not resistant to outliers. |
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Term
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Definition
If our X and Y variables do show a linear
relationship, we can calculate a best fit
line in addition to the correlation
The values a and b together are called
the regression coefficients
• a = intercept
• b = slope
How to determine our “best” line ? (ie. best regression coefficients a and b ?)
• Must square “Y-residuals” and add them up:
total residuals = ∑ (y i -(a + b ⋅ x i )) 2 |
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Term
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Definition
Line with smallest total residuals
Best values for slope and intercept |
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