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Stats 5.1
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Terms in this set (49)
What is r
Correlation coefficient
What does the correlation coefficient measure
Strength, direction, linear relationship between x and y
R is a number between
-1 and 1
r=1 indicates
Perfect positive association
r=-1 indicates
Perfect negative association
R is a measure of
Linear relationship between x and y
What is a and b in y = a + bx
a= y-int and b=slope
Does it matter which variable you call x or y when finding correlation
No
Z scores and r don't have
units
R doesn't change when this changes
Unites of measurement of x, y or both
If x is height then what happens to the relation with the corresponding z score
It doesn't depend on how x is measured
A value of r close to 0 doesn't rule this out since what could be possible
Strong relationship, strong nonlinear relationship between x and y
Correlations requires that both variables are
Quantitative
Correlation is not resistant to
Outliers
A regression line summarizes the relationship between what and when
Two variables when one of the variables helps explain or predict the other
A regression line describes how
A response variable y changes as an explanatory variable x changes
We often use regression line to
Predict y for x
Least squares regression line of y on x is the line that makes this as small as possible
Sum of the squared residuals
Residuals are predicted by
Least squares regression line
The residual is equal to
Observed y - predicted y
Predicted y is symbolized as
Y carrot
Length of the vertical segment from the point to the least squares regression line
Residual
When the residual is negative, the point is
Below the LSRL
When the residual is positive the point is
Above the LSRL
Residual =
Actual - predicted
Form of regression line
y=a+bx
b=
Change in y over the change in x
What is y carrot
Predicted value of response variable for a given value of explanatory variable x
What is the slope b
Amount which y is predicted to change on average when x increases by one unit
A is the y intercept and the predicted value of y when
x=0
The use of regression line for prediction outside of the interval of values of the explanatory variable x used in a like
Extrapolation
We do not know if this happens out of the range of x values
Linear pattern observed in scatterplot continues
Don't make this using values of x that are larger or smaller than those in data
predictions
(X line over, y line over) always
Lies on LSRL
When writing equation of LSRL find this first
B
Y = a + bx becomes
a= y - bx
A scatterplot of the residuals against the explanatory variable
Residual plot
Indicated potential problems in residual plot , this would rather be desired
Unusual observation or patter, no pattern such an a curvature
Curvature in the residual plot is an indication that the relationship between x and y
Isnt linear and a curve would be a better choice that a line
Is sometimes easier to see in residual plot than in scatterplot
Relationship between x and y
If the spread of resids increase/decreases s and x increases/decreases, is a linear model a good fit
No
If the residual plot contain a patter then the line is what kind of fit
Not a good fit
If the residual plot consists on a random scatter of points centered at 0 then the line is what kind of fit
A good fit
What is influential observation
Far removed from the rest of the points and if you remove it then the slope of the line changed
Since the slope has changed, the point is
Influential
It is important to look for these values in resid plot
Unusual
Points that are outliers in y direction but not in x direction have
Large resid
Not all outliers are
Influential
Best way to verify that a point is influential
Find regression line both with and without unus point then look ffor a moveme
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