AP Statistics Unit 2 Study Guide
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scatterplot
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display the relationship between two numerical variables
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correlation coefficient "r"
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the strength, direction, and linear relationship between the x-variable and y-variable
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least square regression line
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line of best fit for the scatterplot; minimizes the sum of the square of the deviations from a line
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explanatory variable
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explains the other variable; causes the response variable to change
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response variable
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response to the other variable; dependant
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extrapolation
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not right; using LSRL to predict values outside of the range of the original data set
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outliers
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points that are far away from the LSRL relative to other points
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influential points
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points that significantly impacts the slope of the LSRL
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lurking variable
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different outside variables that causes both x and y to change
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residual
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y - ŷ
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coefficient of determination "r^2"
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r^2% of the variation in y-variable can be explained by the approximate linear relationship between x-variable and y-variable
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legitimate values
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[-1,1]
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none
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0
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weak
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(-0.5,0) U (0, 0.5)
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moderate
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(-0.8, -0.5) U (0.5, 0.8)
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strong
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[-1, -0.8) U 90.8, 1]
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find the LSRL
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ŷ = 2.544 + 0.164x
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identify the variables
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x = amount of caffeine intake (mg); y = number hours spent studying
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interpret the slope
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when the amount of caffeine intake increases by one, the number of hours spent studying increase by 0.164
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identify the coefficient of determination
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r^2 = 60.032
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interpret the coefficient of determination
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60.032% of the variation in the amount of hours spent studying can be explained by the approximate linear relationship with caffeine intake
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find the correlation coefficient
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r = 0.7748
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interpret the correlation coefficient
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there is a moderately strong, positive, linear relationship between the intake of caffeine and the amount of time spent studying
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slope of LSRL
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for each increase in the "x-variable" of one "x-unit", there is a predicted "increase/decrease" in the "y-variable" of "b constant" "y-units"
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correlation coefficient
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there is a "strength", "direction", linear relationship between "x-variable" and "y-variable"
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correlation of determination
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"r^2"% of the variation in the "y-variable" can be explained by the approximate linear relationship between "x-variable" and "y-variable"
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residual
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the actual "y-variable" is "residual" "y-unit" "above/below" the predicted "y-variable"
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the sum of the residual is always zero
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error = observed - predicted
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residual plots show if the model is appropriate or not between two variables
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if there is no pattern between the points on the residual plot, the model is appropriate
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if there is a pattern between the points on the residual plot, the model is not appropriate
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when the residual plot is not appropriate, you can transform the data points until the plot turns random
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x & log y
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log x & log y
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x & sqrt y
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x & 1/y
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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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