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AP Statistics Chapter 3: Describing Relationships
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3.1: Scatterplots and Correlation 3.2: Least - Squares Regression
Terms in this set (22)
Scatterplot
Shows the relationship between 2 quantitative variables measured on the same individual. The values of one is on the x-axis, and the other is on the y-axis.
Explanatory Variable
Help explain or influence changes in a response variable. The y-axis.
Response Variable
Measures an outcome of a study. The x-axis.
Direction
Positive, negative or no direction.
Form
Linear or not.
Strength
Strong or weak.
Correlation R
Measures the direction and strength of the linear relationships between two quantitative variables.
1. Must be between -1 and 1.
2. r > 0 is positive (near 1).
3. r < 0 is negative (near -1).
4. Near zero, there is a weak relationships.
5. Near -1 or 1, there is a strong relationship.
Outliers
Can influence the correlation tremendously.
Regression Line
Line that describes how a response variable y changes to an explanatory variable x changes used to predict y when x is given.
Slope
b = mean
r = r
SDy = standard deviation of y
SDx = standard deviation of x
Intercept
Where the regression line crosses a x or y-axis.
y-Intercept
Y = mean of all y values
X = mean of all x values
b = mean
Extrapolation
The use of a regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line. Such predictions are accurate.
Least-Squares Regression Line
The line that makes the sum of the square plot as small as possible.
Coefficient by Constant
The y-intercept predictor by root is the slope.
R - Sq = r
Residuals
Difference between an observed value and the expected value.
Residual Plots
No patterns means that the line is good. if there is a pattern, it means that the data is not linear.
Standard Deviation of the Residuals
How far off the numbers are from the expected values. The predicted error. If the SD is small, it is good.
Coefficient of Determination r²
Fraction of a variation is the values of y that is accounted for by the least-squares regression line.
Outliers
The influence of the regression line.
Influential Observation
An outlier that influence that outlier in a great amount.
Guide to Minitab
Coef. by Constant = y-intercept
Coef. by (unit) = slope
S = Standard deviation of the risiduals
R - Sq = r²
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