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AP Statistics Unit 2 Study Guide
Terms to Know
scatterplot 
display the relationship between two numerical variables 
correlation coefficient "r" 
the strength, direction, and linear relationship between the xvariable and yvariable 
least square regression line 
line of best fit for the scatterplot; minimizes the sum of the square of the deviations from a line 
explanatory variable 
explains the other variable; causes the response variable to change 
response variable 
response to the other variable; dependant 
extrapolation 
not right; using LSRL to predict values outside of the range of the original data set 
outliers 
points that are far away from the LSRL relative to other points 
influential points 
points that significantly impacts the slope of the LSRL 
lurking variable 
different outside variables that causes both x and y to change 
residual 
y  ŷ 
coefficient of determination "r^2" 
r^2% of the variation in yvariable can be explained by the approximate linear relationship between xvariable and yvariable 
Strength of "r" (Correlation Coefficient)
legitimate values 
[1,1] 
none 
0 
weak 
(0.5,0) U (0, 0.5) 
moderate 
(0.8, 0.5) U (0.5, 0.8) 
strong 
[1, 0.8) U 90.8, 1] 
LSRL Example
Desiree is interested to see if students who consume more caffeine tend to study more as well. She randomly selects 202020 students at her school and records their caffeine intake (mg) and the number of hours spent studying. A scatterplot of the data showed a linear relationship.
This is computer output from a leastsquares regression analysis on the data.
LSRL Example Interpretations
find the LSRL 
ŷ = 2.544 + 0.164x 
identify the variables 
x = amount of caffeine intake (mg); y = number hours spent studying 
interpret the slope 
when the amount of caffeine intake increases by one, the number of hours spent studying increase by 0.164 
identify the coefficient of determination 
r^2 = 60.032 
interpret the coefficient of determination 
60.032% of the variation in the amount of hours spent studying can be explained by the approximate linear relationship with caffeine intake 
find the correlation coefficient 
r = 0.7748 
interpret the correlation coefficient 
there is a moderately strong, positive, linear relationship between the intake of caffeine and the amount of time spent studying 


Interpretations
slope of LSRL 
for each increase in the "xvariable" of one "xunit", there is a predicted "increase/decrease" in the "yvariable" of "b constant" "yunits" 
correlation coefficient 
there is a "strength", "direction", linear relationship between "xvariable" and "yvariable" 
correlation of determination 
"r^2"% of the variation in the "yvariable" can be explained by the approximate linear relationship between "xvariable" and "yvariable" 
residual 
the actual "yvariable" is "residual" "yunit" "above/below" the predicted "yvariable" 
Residuals and Residual Plots
the sum of the residual is always zero 
error = observed  predicted 
residual plots show if the model is appropriate or not between two variables 
if there is no pattern between the points on the residual plot, the model is appropriate 
if there is a pattern between the points on the residual plot, the model is not appropriate 
when the residual plot is not appropriate, you can transform the data points until the plot turns random 
Residual Plot Examples
the top residual plot is appropriate because the points are random while the bottom residual plot is not appropriate because there is a pattern between the points
NonLinear Transform Data
x & log y 
log x & log y 
x & sqrt y 
x & 1/y 
Correlation Doesn't Imply Causation
If we collect data for the total number of Master’s degrees issued by universities each year and the total box office revenue generated by year, we would find that the two variables are highly correlated.
Correlation Doesn't Imply Causation Explanation
Does this mean that issuing more Master’s degrees is causing the box office revenue to increase each year? Not quite. The more likely explanation is that the global population has been increasing each year, which means more Master’s degrees are issued each year and the sheer number of people attending movies each year are both increasing in roughly equal amounts. Although these two variables are correlated, one does not cause the other. 

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