Describing Relationships in Two Variable Data

doesn't change

because r uses the standardized values (z-scores) of the observations, r _______ __________ when we change the units of x or y (or both)

curved

correlation DOES NOT describe (linear/curved) relationships -choose one in parentheses

causation

correlation DOES NOT imply...

x and y

correlation makes no distinction between ____ and _____, which means that the strength of the pattern won't change

quantitative

correlation requires that BOTH variables be (categorical/quantitative) -choose one in parentheses

strength

describing if the scatterplot has a strong, moderate, or weak pattern

outliers

describing if the scatterplot has any data point that is far from the overall pattern

form

describing if the scatterplot looks linear or curved, and if it has clusters

direction

describing if the slope of the scatterplot is positive or negative

no

does the correlation have a unit of measurement?

extrapolation

making predictions for values outside of the domain of the data set -risky because we don't know for sure that the relationship will stay linear unless we have data to support that statement

least squares regression line (LSRL)

minimizes the sum of the squares of the vertical distances from the points on the line

scatterplot

shows the relationship between two quantitative variables measured on the same individuals

r²

the coefficient of determination; this percentage measures how closely the points fall to the LSRL and therefore provides an indication of how confident one can be in predictions made with the line

r

the correlation coefficient; measures the strength and direction of the linear relationship between two quantitative variables

resistant

the correlation is affected by outliers like the mean and standard deviation are, which means it is not...

-1 and 1

the correlation is always a number between...

residual

the prediction error; the "leftover" part of the data as a result of chance variation or variables not measured equation: actual y value - predicted y value

lurking variables

variables not among the explanatory or response variables that influence the relationship between those variables

explanatory variable

x, or the independent variable

response variable

y, or the dependent variable