Exam 2 - Statistics Flashcards
what measures the outcome of a study
response variable
what explains or causes changes in the response variables
explanatory variable
what kind of plot shows the relationship between two quantitative variables measured on the same individuals
scatterplot
when above-average values of one tend to accompany above-average values of the other and below-average values also tend to occur together
positive association
when above-average values of one tend to accompany below-average values of the other, and vice versa
negative
the direction and strength of the linear relationship between two quantitative variables
correlation
the magnitude of r
strength
if the correlation is zero, then the slop of the least-squares regression line is
zero
b1
slope
b0
intercept
what is the straight line formula
y(hat) = b0+b1x
a straight line where we have data on an explanatory variable and a response variable
least-squares regression line
slope’s equation
b1=rSy/Sx
intercept equation
b0=y-b1x
square of the correlation
r^2
the fraction of the variation in the values of y that is explained by the least-squares regression of y on x
r^2
the use of a regression line for prediction far outside the range of values of the explanatory variable x used to obtain the line
extrapolation
the difference between an observed value of the response variable and the value predicted by the regression line
residuals
if the regression line is a good fit for the data, then
no obvious pattern should be shown in the residual plot
an observation that lies outside the overall pattern of other observations
outliers
points that are outliers in the y direction of a scatterplot have…
large regression residuals
If removing an observation for a statistical calculation markedly changes the result of the calculation then it is
influential
an association or comparison that holds for all of several groups can reverse direction when the data are combined to form a single group
simpson’s paradox
when two variables effects on a response variable cannot be distinguished from each other
confounding
confounded variables can be either
explanatory variable or lurking variable
the observed association between the variable x and y is explained by a lurking variable z
common response
the strength of the association influences the …?
precision of determining the value of the other variable
correlation makes no distinction between
explanatory and response variables
r has no
units
correlation requires that both variables be
quantitative
error =
y-b0-b1x
so error =
y - y(hat)
error = noise =
distance = residual
residual =
observed y - predicted y
outliers in y direction are
residuals (large)
outliers in x direction are
influential
data =
signal + noise
r^2 =
variations explained by model/total variations
total variations =
variation explained + unexplained