Assignment 7

Q1. The data for this question come from the US Historical Climatology network. They are the annual mean temperatures (in degrees F) in Ann Arbor going back about 150 years.
  1. Is there a linear trend?
  2. Observations in successive years may be correlated. Fit a model that estimates this correlation. Does the change your opinion about the trend?
  3. Fit a polynomial model with degree 10 and use backward elimination to reduce the degree of the model. Plot your fitted model on top of the data. Use this model to predict the temperature in 2020.
  4. Suppose someone claims that the temperature was constant until 1930 and then began a linear trend. Fit a model corresponding to this claim. What does the fitted model say about this claim?
  5. Make a cubic spline fit with 6 basis functions evenly spaced on the range. Plot the fit in comparison to the previous fits. Does this model fit better than the straight line model?
(This is just a single dataset. Obviously it would be foolish to make any conclusions on global warming based on just this data).@

Q2. Assessors in the metropolitan area of Minneapolis-St. Paul are bound by law to value farmland enrolled in a "Green Acres" program only with respect to its value as productive farmland; the fact that a shopping center or an industrial park has been built nearby cannot enter into the valuation. This creates difficulties because almost all sales, which are the basis for setting assessed values, are priced according to the development potential of the land, not its value as farmland. As an aid to setting assessed values, a method of "equalizing" valuation of land of comparable quality was needed. Some data give one possible method of equalization, based on the computed soil productivity score, a number between 1 and 100, with higher numbers corresponding to better land. The unit of analysis is a township. For each township with tillable land, the average soil productivity score P and the 1981 and 1982 average assessed value per acre were recorded. The data are from four counties located south and west of Minneapolis where development pressures have little effect on land values.

Come up with a method for the assessors to use in assessing farmland values in the Minneapolis area using the soil productivity score.

Q3. Apply the Box-Cox approach to the model in problem 2 (ii) of Assignment 2, to find an appropriate transformation for the dependent variable.