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Chapter 6 Closure (Direction (If one variable decreases as the other…
Chapter 6 Closure
Direction
If one variable decreases as the other variable increases, there is said to be a negative association. If there is no apparent pattern in the scatterplot, then the variables have no association.
If one variable in a relationship increases as the other variable increases, the direction is said to be a positive association.
When describing a linear association, you can use the slope, and its numerical interpretation in context, to describe the direction of the association.
correlation coefficient
r^2= a percent
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The correlation coefficient squared, and usually expressed as a percent.
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Its interpretation is that R2% of the variability in the dependent variable can be explained by a linear relationship with the independent variable.
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Association
Possible association between two categorical variables can be studied in a conditional relative frequency table. Also see scatterplot.
A relationship between two (or more) variables. An association between numerical variables can be displayed on a scatterplot and described by its form, direction, strength, and outliers.
Model
A mathematical summary (often an equation) of a trend in data, after making assumptions and approximations to simplify a complicated situation. Regressions are a type of model. Also see regression.
Models allow us to describe data to others, compare data more easily to other data, and allow us to make predictions.
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Residual
A residual can be graphed with a vertical segment that extends from the observed point to the line or curve made by the best-fit model.
The residual is the y-value predicted by the best-fit model subtracted from the actual observed y-value.
Form
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A residual plot can help determine if a particular form is appropriate for modeling the relationship.
Residual Plot
A display of the residuals of an association. A residual plot is created in order to analyze the appropriateness of a best-fit model.
If a model fits the data well, no apparent pattern will be made by the residuals—the residuals will be randomly scattered.
Lower bound
The lowest value that a prediction is likely to be. The lower bound is determined by the lower boundary line.
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LSRL
(least squares regression line) A unique best-fit line that is found by making the squares of the residuals as small as possible.
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Upper bound
The highest value that a prediction is likely to be. The upper bound is determined by the upper boundary line.
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