1. Chapters 7 -10 Important Concepts and Terms
AP Stats Review Unit II
Chapters 7 -10
Important Concepts and Terms

2. 2.1 Scatter Plots
Response Variable – Measures an outcome of a study. Explanatory Variable – Explains or causes change in the response variable

3. Scatter Plots
Scatter Plots Shows the relationship between two quantitative variables measured on the same individuals. The explanatory variable (if there is one) always goes on the horizontal axis, the response on the vertical axis.

4. Examining a Scatterplot
Look for an overall pattern and striking deviations from the pattern
Describe pattern using form, direction and strength of the relationship DFS
Look for outliers
Look for positive or negative association (slope)

5. 2.2 Correlation
Correlation measures the direction and strength of the linear relationship between two quantitative variables. Usually written as r.
FORMULA

6. Properties of Correlation
Makes no distinction between explanatory and response variables
Both variables need to be quantitative
Does not change when data is subjected to a linear transformation such as move 3 left or 2 down
Positive r indicates positive association, Neg. r indicates neg. association
r always lies between -1 and 1 values near 0 indicate a very weak linear relationship. Values of r that lie close to -1 or 1 indicate the points lie close to a straight line
No units
Nonresistant

7. 2.3 Least Squares Regression
Regression Line A straight line that describes how a response variable y changes as an explanatory variable x changes. This is used to predict the value of y for a given value of x. Regression unlike correlation requires an explanatory and response variable.

8. Least Squares Regression Line
The line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible.

9. Equation of the Least-Squares Regression Line Equation:
Slope b:
This is the rate
of change
Intercept a:
This is the value
when x=0

10. Points to Remember:
The slope b of the LSRL is the rate of change, for each one unit in x, this is what y changes by.
The correlation r represents how close to a straight line the points lie.
The y-intercept tells us what y is when x is zero.

11. r-squared
The percent of the variation in the values of y that is explained by the LSRL of y on x.

12. Residuals A residual is the difference between an observed value of the response variable and the value predicted by the regression line residual=observed y – predicted y

13. Residual Plots
A scatterplot of the regression residuals against the explanatory variable.

14. Lurking Variable A variable that has an important effect on the relationship among the variables in a study but is not included among the variables studied. VERY SCARY

15. Warnings
Correlation measures linear association. Plot your data to make sure the relationship is linear.
Extrapolation (predicting far outside the domain of data) can produce unreliable predictions.
Correlation and Least Squares Regression LINE are not resistant to outliers.
Lurking variables can make a correlation or LSRL unreliable
Association does not imply causation, strong association between variables does not imply that changes in one causes the other to change

16. 2.5 Exponential Growth
Linear versus Exponential Growth Linear: Increases by a fixed amount in each equal time period. Graphs are straight lines. Exponential: Increases by a fixed percentage of the previous total. Graphs are curves.

17. Logarithm Transformation If a variable grows exponentially, its logarithm grows linearly. Var x=2 Log x=

18. Exponential versus Power
Exponential curved pattern
Linear relationship between x and log y
Common ratio between y values
Does not go through origin
Power curved pattern
Linear relationship between logx and logy
Searching for the perfect power to fit the curve
Goes through origin
These are options to re-express the data to make the scatterplot more linear. Then use power ten to get predictions.

19. The 3 R’s Republicans: Romney and Ryan little side note (Mitt Romney, the next American President) only my prediction
When you are asked to explain why your model will provide reliable predictions or why it is so good then always point out the three R’s
R close to 1 or -1
R squared close to 100%
Residual Plot - You need this to be random in order to justify your choice. This way some residuals are positive and some are negative and not many points are too far from your model.