## AP Statistics: Chapter 3 – Examining Relationships

response variable

A variable that measures the outcome of a study.

explanatory variable

A variable that helps explain or influences changes in a response variables.

dependent variables

Another term for “response variable.” Related to algebra.

independent variables

Another term for “explanatory variable.” Related to algebra.

scatterplot

A graph showing the relationship between *two quantitative variables* measured on the *same individuals.* Uses a horizontal and a vertical axis; the horizontal is an explanatory variable if the explanatory-response distinction is made.

direction

Is the scatterplot a positive or a negative correlation? This is the term we use to describe that.

form

The general look of a relationship on a scatterplot: Is it completely linear? Is it curved slightly?

clusters

On a scatterplot these are areas where the data congregates especially heavily. You should make an attempt to explain their existence.

strength of relationship

How closely do the points on a scatterplot follow a clear form? This is the term for measuring that in general, related to least-squares regression’s /r/ value.

correlation (r)

A measurement of the direction and strength of a linear relationship between two quantitative variables. Extremely important!

n (It really doesn’t give a hoot which variable you call x and y in the equation)

Does correlation distinguish between explanatory and response variables? [yn]

n (r uses standardized values, so it doesn’t matter.)

Does r change when we change the units of measurement of the variables? [yn]

r > 0

When does r indicate a positive correlation? [_ _ _]

-1, 1

r is always between what two values? [_, _]

regression line

A line that describes how a response variable changes as an explanatory variable changes. We often use these to predict values of the RV for a given value of the EV.

extrapolation

The use of a regression line for prediction outside the range of values of the EV used to obtain the line. Oftentimes, these extrapolated values are not 100% accurate – but they’re still handy.

least-squares regression line

The regression line that makes the sum of the squared vertical distances of the data points from the line as small as possible. In other words: {http://www.dynamicgeometry.com/images/advancedSketchGallery/statistics/leastsq.gif}

residual

The difference between an observed value of the response variable and the value predicted by the regression line.

residual plot

A scatterplot of the regression residuals against the explanatory variable [EV]. Useful for seeing how closely a regression line fits the data.

coefficient of determination

The fraction of variation in the values of the response variable [RV] that can be explained by the least-squares regression line.

y (Least-squares regression uses the distances of the y variable. If you switch them, you get a different regression line. That’s no good!)

Is the distinction between explanatory and response variables significant in regression? [yn]

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