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AP Stats Unit 9: Linear Regression Inference Vocab + Variables

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To review: we use least-squares regression to study the relation between a couple of variables, both of which are (quantitative, categorical).
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To review: we use least-squares regression to study the relation between a couple of variables, both of which are (quantitative, categorical).
Quantitative
Before doing regressions to study the relationship between two quantitative variables, we should explore the data by examining a _______ and a __________.
(1) Scatterplot
(2) Residual plot
The statistic that describes the strength of a linear relationship, that is the same whichever variable is thought of as the explanatory variable, and which has a familiar relationship to the percent of variance in one variable explained by the other, is the ______ ______.
Correlation coefficient (or just, the correlation)
What is a residual?
A residual is the vertical distance between the data point and the regression line, or y - ŷ.
The r-squared (r²) value, which is part of the regression output, tells us how much of what is what?
How much of the variation in the y variable is accounted for by the linear relationship with x.
Suppose we draw lots of samples and compute a regression line for each sample. The slope and intercept of each sample line estimates a true value. Thus the slope and intercept we obtain from our sample are _____ that estimate population ______.
(1) Statistics
(2) Parameters
One of the conditions for regression inference is that for any fixed value of x, the response variable y varies according to a _____ distribution.
Normal
Another assumption for regression inference is that for any fixed value of x, the repeated responses y are ____ of each other.
Independent
Another assumption for regression inference is that the means of the sets of y-values for each x value have what relationship to the x values?
That the means of the y's for each x are a linear function of x: mean for y's = alpha + beta * x

(µy = α + β(x))
Another assumption for regression inference is that what measure of dispersion is equal for each value of x?
The standard deviation of the y's for the various x values.
True or False: the slope and intercept we obtain from the least squares regression for our sample are unbiased estimators, respectively, of the line connecting the population means for each of the x's.
True
What is the unbiased estimator for the standard deviation of the y values around the regression line (in other words, the standard deviation of the y values around the means of each of those values for each x)?
The statistic called s, which is the standard error, or the standard deviation of the residuals.
The statistic s represents the estimate of the standard deviation ____ in the regression model.
σ
The parameter we are usually most interested in estimating from regression output is the (slope, y- intercept) of the line.
slope
What is the general form for a confidence interval for regression slope?
b ± t*SEb

(the second b for be subscript)