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What does the regression line summarize?
The relationship between two variables.
What does a regression line help to do specifically?
To help predict a response value y when given explanatory variable x.
What type of line represents regression.
A strait line.
What is the equation for a regression line? What it is the same as?
y = mx + b
What does a regression line not say about the relationship between two variables?
It can't tell you the importance between two variables.
What does the least-squares regression line make as small as possible?
The vertical distances of the data points from the line.
What is prediction error? What is the equation?
The value between observed y and regression value y.
Error = observed response - predicted response
What is meant by y hat?
The predicted value of y.
What is essential to know w/ regression?
One should always be aware between the explanatory and response variables.
What is the relationship between slope and correlation?
Both will always have the same sign.
What point does the least-square regression line always pass through?
(x bar, y bar)
What is r?
The strength of the correlation between two variables.
What is r
? How is it calculated?
measures the fraction of the variation in the values of y that is explained by the least-squares regression of y on x.
Does a regression line explain all of the variation between two variables?
Where does the usefulness of the line for prediction come from?
Comes from the strenght of the relationship, which is measured by r
What is a residual? What is it's equation?
The difference between an observed value of the response variable and the value predicted by the regression line (also the prediction error).
= y - yhat
What is a special property of residuals of least-squares line?
The mean of the least-squares residuals is always 0.
What is an influential observation?
An observation that markedly changes the strength of the relationship between two variables.
Information from statistics text book on regression. Taken from chapter 5.