The relationship between two variable can be _______influenced by _____variables that are _____in the background.
strongly,other,lurking
Response Variable
measures an outcome of a study(dependent variable)
Explanatory Variable
helps explain or influences changes in a response variable (independent variable)
The ____ variable depends on the ______variable.
response, explanatory
Remember that calling one variable explanatory and the other response ______necessarily mean that changes in one _____ changes in the other.
dosent, cause
What is the most effective way to to display the relationship between two quantitative variables?
A scatterplot
Scatter plot
shows the relationship between two quantitative variables measured on the same individuals.
direction
the overall pattern moves from upper left to lower right. positive or negative association
How is a strength of a relationship in a scatter plot determined?
by how closely the points follow a clear form
How do you interpret a scatter plot?
-look for the overall pattern and for striking deviations from that pattern
-you could describe the overall pattern of a scatter plot by the direction, form, and strength of the relationship
-An important kind of deviation is an outlier, an individual val
negatively associated
When above-average values of one tend to accompany below-average values of the other, and vice versa.
positively associated
when above average values of one tend to accompany above-average values of the other and below average values also tend to occur together
Our eyes are __ good judges of how strong a linear relationship is.
not
correlation measures
the direction and strength of the linear relationship between two quantitative variables.
Correlation is written as
r
correlation is not____
resistant, r is strongly affected by a few outlying observations, use r with caution if outliers appear
Correlation makes __distinction between explanatory and response variables.
no, it makes no difference which variable you call x and which variable you call y
Because r uses the standardized values of the observations, r does __change when we change the units of measurement of x, y, or both.
not, the correlation r itself has no unit of measurement, it is just a number
positive r indicates positive association between the variables and negative r indicates negative association
...
the correlation r is __a number between -1 and 1.
always
Correlation requires that both variables be _______so that it makes sense to do the arithmetic indicated by the formula for r.
quantitative
Correlation measures the strength of only the linear relationship between two variables.
correlation does not describe curved relationships between variables, no matter how strong they are
correlation is not a complete summary of two-variable data
give means and standard deviations of both x and y along with the correlation
form
linear relationships
strength
the strength of a relationship is determined by how close the points in the scatterplot lie to a simple form such as a line
regression line
summarizes the relationship between two variables
what does regression require?
you have an explanatory variable and a response variable
We use a regression line
to predict the value of y for a given value of x
Regression Line=
a+bx
slope
the amount by which y changes when x increases by one unit,
you ___say how important a relationship is by looking at how big the regression slope is
cant
Extrapolation
the use of the regression line for prediction outside the range of values of the explanatory variable x used to obtain the line. Such predictions are often not accurate
least-squares regression line
of y on x is the line that makes the sum of the squared vertical distances of the data points from the line as small as possible
least squares regression line equation =
^y =a+bx with slope b=r(standard deviation of y/ standard deviation of ) that passes through point (xbar,ybar)
residuals
The difference between the observed value of the response variable and the value predicted by the regression line residual= observed y- predicted y
what is the sum of the least squares residuals?
0
what do residual plots help you asses?
how well a regression line fits the data
the residual plot should should no obvious __.
Pattern
Increasing(or decreasing) spread about the line as x increases indicates that prediction of y will be less accurate for larger x(smaller x)
...
Coefficient of Determination(r^2)
numerical quantity that tells us how well the least squares line does at predicting values of the response variable y.
you read slope as:
a change of one standard deviation in x corresponds to a change of r standard deviation in y
Correlation and regression describe only___relationships
linear
An observation is influential for a statistical calculation
if removing it would markedly change the result of the calculation
Lurking Variable
A variable other than x and y that simultaneously affects both variables, accounting for the correlation between the two
Correlations based on averages are usually too___ when applied to individuals
high