SWBAT: Calculate and interpret the residual plot for a line of regression Do Now: Do heavier cars really use more gasoline? In the following data set,

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SWBAT: Calculate and interpret the residual plot for a line of regression Do Now: Do heavier cars really use more gasoline? In the following data set, x is the weight of some randomly selected cars (in hundreds of pounds), and y is the gas mileage (in mpg) for that car. This data set comes from Consumer Reports (vol. 62, no.4). Calculate the equation of the least-squares regression line and interpret the slope and y-intercept in the context of the data. (Give your answer to 3 decimal places.)

SWBAT: Calculate and interpret the equation of the least-squares regression line and interpret residual plots Residual Plot A residual plot is a scatterplot of the residuals against the explanatory variable (x). A residual plot’s purpose is to determine how well a regression line fits the data. Does a ______________ association exist between x & y? *The residual plot should show no obvious patterns and should be relatively small in size. *The residuals should be relatively small in size

SWBAT: Calculate and interpret the equation of the least-squares regression line and interpret residual plots Standard deviation of the residuals (s) This value estimates the “typical” or “average” prediction error (residual) from the regression line. Coefficient of determination (r 2 ) The percent variation in the values of y that is accounted for by the least-squares regression line of y on x. **

SWBAT: Calculate and interpret the equation of the least-squares regression line and interpret residual plots Example: Using the least-squares regression equation from the Do Now (a) Find and interpret the correlation coefficient and the coefficient of determination: r = r 2 = (b) Create a residual plot. Does the plot show a linear relationship? (c) Determine the standard deviation of the residuals (s) and interpret this value in the context of the problem.