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Linear Regression Review
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Terms in this set (65)
How to find a regression line on calculator
STAT/CALC/LIN REG L1, L2, Y1 (VARS/Y-Vars/1/1)
Slope of a regression line
b1=r(Sy/S/x)
r tells the ____ of a linear relationship
Strength and direction
r is always between what two values (inclusive)?
1 and -1
Graphs with positive slopes have ___ r values; graphs with negative slope have ____ r values.
Positive; negative
How to find a residual
Residual = observed - predicted
The mean of the residuals
0
What does the best fit line do?
Minimizes the sum of the square of the residuals
A residual plot shows the residuals on the ____ axis.
Y axis
A residual plot shows the explanatory values on the ___ axis.
X axis
Points with large residuals are called
Outliers
Points which change the slope of the line and correlation coefficient greatly when removed are called
Influential points
Slope in context
"For every (decrease/increase) of one (unit) in (context of x), there is an average (decrease/increase) in (context of y) of (slope)(units)."
Y-intercept in context
"When the (context of x) is 0 units, I would or predict that the (context of y) would be (y-intercept)."
Correlation coefficient (r) in context
"The correlation coefficient of ____ indicates that there is a (strong/moderate/weak), (positive/negative) linear relationship between (context of y) and (context of x)."
Coefficient of determination (r^2) in context
"(r^2)% of the variability in the (context of y) can be explained by the linear association with (context of x)."
Residual plot in context
"The residual plot is (randomly scattered/has a pattern) indicating that a linear model (is/is not) appropriate."
The explanatory variable goes on which axis of a scatter plot?
The x (EXplanatory)
The response variable goes on which axis of a scatter plot?
Y axis
Direction
Positive or negative
Form
Linear, exponential, parabolic, etc.
Strength
How closely the points follow a line or curve
Extrapolation
Using a regression line to predict an out of range number
Least-squares regression line
Line that makes the sum of the squared residuals as small as possible
How to find a regression line on calculator
STAT/CALC/LIN REG L1, L2
r
"The correlation coefficient of ____ indicates that there is a (strong/moderate/weak), (positive/negative) linear relationship between (context of y) and (context of x)."
Negative association
High x values with low y values
Extrapolation
Using a regression line to predict an out of range number
Least-squares regression line
Line that makes the sum of the squared residuals as small as possible
Bivariate data
Data with 2 quantitative variables.
Scatterplot
A graph that shows the relationship between a data set with two quantitative variables graphed as ordered pairs on a coordinate plane.
Positive association
An association in which the y-value increases as the x-value increases.
Negative association
An association in which the y-value decreases as the x-value increases.
No association
Where there is no pattern in the observed data.
Linear association
An association in which the data appear to lie close to a line.
non-linear associaiton
Where data points follow a curved pattern.
r
Correlation; has no unit, it is just a measure of correlation on a scale of -1 to 1
Correlation (definition)
The direction and strength of the linear relationship between two quantitative variables.
When not to use "r"
When a scatter plot is NOT linear
Scatterplot
The most useful graph for comparing two quantitative variables against one another
The five parts of interpreting a scatterplot
Direction, form, strength, unusual features, CONTEXT
Strength of data in a scatterplot
Strong, moderate, weak (the stronger it is, the closer pattern there is)
Unusual features in a scatterplot
Possible outliers, clusters, vertical or horizontal stacks
Least squares regression line (LSRL)
The line that makes the sum of the squared residuals as small as possible.
LinReg (a+bx), Linear regression line, Regression line, line of best fit
Alternate names for the least squares regression line
"Hat" on a variable
The variable is estimated (â means prediction of a)
Extrapolation
Predicting a value outside of a given data set
When is it a good idea to extrapolate?
If predicting a future event that has an x value close to the other x values
Interpolation
Predicting a value inside of a given data set
Residual
The difference between an actual value and its predicted value
(a-â)
Residual plot
Plot to determine curves; X axis features the same explanatory variable inputs, y axis shows residuals of points with 0 residual in the middle
Why use a residual plot?
Residual plots act as magnifying glasses to show curves or true linearity in a scatterplot where the curve is otherwise unidentifiable.
When to use a linear model
Only if there is random scattering in the residual plot
Variable s
Standard deviation of residuals of a scatterplot
Correlation does not necessarily imply
Causation
Correlation cannot exist with a
categorical variable
Rule of thumb border lines for saying weak, moderate, strong in terms of correlation
Between .5 and -.5 is weak; .5001-.8 is moderate; >0.8 or <-0.8 is strong. Very weak, Moderately strong and moderately weak and very strong are judgement calls based on these ranges.
Positive correlation
Relationship in which increases in the values of the first variable are accompanied by increases in the values of the second variable.
Residuals
Difference between the observed value of the response variable and the value predicted by the regression line; can be positive or negative.
Outlier
Observation with an unusually large residual; its pairs of values do not follow the overall pattern of the regression equation
Predicted Value
Estimated value of the response variable predicted by a regression model for a given explanatory variable; denoted by y-hat
interpreting slope
for every increase of one (context of x), there is a predicted (increase,decrease) in (context of y) of (slope with units)
interpreting y intercept
when the (context of x) is 0 (unit), I would predict that the (context of y) would be (y-intercept)
interpreting correlation coefficient
The correlation coefficient of _________ indicates that there is a (strong, moderate, weak), (positive,negative) linear relationship between (context of y) and (context of x)
interpreting coefficient of determination
(r²%) of the variability in (context of y) can be explained by the linear association with (context of x)
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