(16)Most of the farms in this survey have fewer than 1000 acres of wheat planted, while a few others are much larger (up to about 1400 acres). This skewness in the number of acres planted a)Violates the normality assumption of the simple regression model. b)Produces a lack of constant variance in the response. c)Introduces dependence in the underlying model errors. d)Implies that the simple regression model omits an important predictor. e)Has produced a few leveraged observations. (17)An extension of this model developed by the Department of Agriculture adds 1 other predictor, increasing R2to 0.75. This revised model, assuming it satisfies the MRM, would be able to predict the wheat production of a typical individual farm with 95% probability to within about
Statistics 621, Final Exam -6- Q1, 2008 (18) The diagnostic plot shown above graphs the residuals from the fitted model of Wheaton Acres. This diagnostic plot indicates that (19) Suppose that the Department of Agriculture were to conduct a second survey, only this time sampling 400 farms rather than 100 farms from the same population as the current survey. In a simple regression of Wheaton Acresusing the data from this larger survey we should expect to find that, in comparison to the shown simple regression, (20) When expanding the scope of the shown survey, if the Department of Agriculture accepts the validity of the simple regression model for all US farms and wants to improve the accuracy of the estimated slope by the most possible, it should seek to a)Remove small farms that plant less than 650 acres of wheat. b)Add more typical farms with about 1,000 acres of wheat planted. c)Add more farms that plant the average number of acres of wheat. d)Add farms that plant a wider range of acres of wheat than those in this survey. e) Add farms that are adjacent to and of similar size as those in the shown model.
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