Home
Browse
Create
Search
Log in
Sign up
Upgrade to remove ads
Only $2.99/month
Chapter 7: Linear Regression
STUDY
Flashcards
Learn
Write
Spell
Test
PLAY
Match
Gravity
This covers all the terms from Chapter 8, as well as some additional terms in the "What Have We Learned?" section. Note that the symbol y^ is y with a triangle-shaped line over it. The symbol y^- is y with a horizontal line above it; same for x.
Terms in this set (12)
Slope of the line
Provides a value in "y-units per x-unit."
(Formula: b1= rsy/sx, where 1,s, and x are subscripts)
Model
An equation/formula that simplifies and represents reality.
Linear model
Equation of a line; to interpret, we must know the variables (along with their W's) and their units.
Predicted value
Value of y^ found for a given x-value in the data; found by substituting the x-value in the regression equation; these are the values of the fitted line- the points (x, y^) all lie exactly on the fitted line
Residuals
Differences between data values and the corresponding values predicted by the regression model- or, more generally, values predicted by any model ( =observed value- predicted value=e=y-y^)
Least squares
This criterion specifies the unique line that minimizes the variance of the residuals or, eventually, the sum of the squared residuals
Regression to the mean
Because the correlation is always less than 1.0 in magnitude, each predicted y^ tends to be fewer SDs from its mean than its corresponding x was from its mean.
Regression to the line of best fit
Particular linear equation (y^=bo=b1x (o and 1x are subscripts)) that satisfies the least squares regression line. Casually, we often just call it the regression line, or the line of best fit.
Slope
b1 (1 is subscript) gives a value in "y-units per x-unit," changes of one unit in x are associated with changes of b1 units in predicted values of y. The slope can be found as the slope of the correlation.
Intercept
gives a starting value in y-units; at the y^ value x is 0. Formula (b0= y^- - b1x^-)
se (e is subscript)
Standard deviation of residuals is found by se= (square root of Σe^2/n-2); when assumptions and conditions are met, the residuals will be described by this SD and the empirical rule.
R^2
R^2 is the square pf the correlation between y and x; gives fraction of variability of y accounted for by the least squares linear regression on x
THIS SET IS OFTEN IN FOLDERS WITH...
Chapter 6: Exploring Relationships Between Variabl…
10 terms
Chapter 8: Regression Wisdom
5 terms
Chapter 1: Stats Start Here
16 terms
Chapter 3: Displaying and Summarizing Quantitative…
26 terms
YOU MIGHT ALSO LIKE...
Chapter 8: Linear Regression
11 terms
Chapter 7-10
24 terms
AP Stats Vocab (7,8,9,10)
23 terms
Unit 2 vocab
22 terms
OTHER SETS BY THIS CREATOR
Geometry Chapter 2
7 terms
Chapter 1 Vocab (Angles)
12 terms
Chapter 5: The Standard Deviation as a R…
13 terms
Chapter 21: Comparing Two Proportions
5 terms