1) Analyze U.S. Department of Agriculture farm data and explore the relationship between the number of U.S. farms (x) and average farm size (y). Estimate a simple linear regression and interpret it. Identify at least one potential federal policy implication based on your analysis.
2) A power company located in southern Alabama wants to predict the peak power load (i.e., the maximum amount of power that must be generated each day to meet demand) as a function of the daily high temperature (X). A random sample of 25 summer days is chosen, and the peak power load and the high temperature are recorded each day.
- a) Create a scatterplot for these data. Comment on the observed relationship between Y and X.
- b) Estimate an appropriate regression equation to predict the peak power load for this power company. Interpret the estimated regression coefficients.
- c) Analyze the estimated equation’s residuals. Do they suggest that the regression equation is adequate? If not, return to part b above and revise your equation. Continue to revise the equation until the results are satisfactory.
- d) Use your final equation to predict the peak power load on a summer day with a high temperature of 100 degrees.
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