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 ID: 696180
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Slide1
SWBAT: Calculate and interpret the residual plot for a line of regressionDo 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.)Slide2
SWBAT: Calculate and interpret the equation of the least-squares regression line and interpret residual plotsResidual PlotA 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 sizeSlide3
SWBAT: Calculate and interpret the equation of the least-squares regression line and interpret residual plotsStandard 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.
**Slide4
SWBAT: Calculate and interpret the equation of the least-squares regression line and interpret residual plotsExample: Using the least-squares regression equation from the Do Now Find and interpret the correlation coefficient and the coefficient of determination:r =r2=
(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.