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But here, the mean MPGCity when weight equals zero is an extrapolation. Besides the physical impossibility of a car having zero weight, there are no cars under 1500 pounds in the data set. Here the intercept is not really interpretable. (e) (i) Narrow. (ii) Not change at all. (iii) Stay about the same. (f) The residual plot suggests that the linearity assumption is violated. The mean of the residuals for small weights of cars and large weights of cars appears to be above zero and for medium weights of cars is below zero. There is no clear violation of constant variance. The normality assumption appears to be violated because a few of the points go a little bit outside of the 95% confidence bands. To remedy the nonlinearity, I would suggest a transformation of X to  EMBED Equation.3 , log X or 1/X and/or a transformation of Y to  EMBED Equation.3 , log Y, or 1/Y (these are the transformations suggested by Tukeys Bulging rule. (g) From the JMP output, an approximate 95% prediction interval is (9.5, 18) miles per gallon. (h) Under the simple linear regression, the distribution of MPGCity for cars of weight 4000 pounds is normal with mean  EMBED Equation.3  and standard deviation  EMBED Equation.3 . Using the least squares estimates  EMBED Equation.3  of  EMBED Equation.3  respectively, the distribution of MPG City given weight=4000 is approximately normal with mean  EMBED Equation.3  and standard deviation 2.168, and thus  EMBED Equation.3  2. (a) The residuals for small areas (area=10) are almost all less than zero while the residuals for area=100 are almost all greater than zero. (b) Using the criterion of looking at the RMSE on the original scale, transformation (ii) of X to log(X) and Y to log(Y) is better (RMSE = 22.71 compared to 27.29 for transformation (i)) (c) The predicted number of species for an island of area 200 is  EMBED Equation.3  'Z[nopq  ! 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