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