- Is there a linear trend?
- Observations in successive years may be correlated. Fit a model that estimates this correlation. Does the change your opinion about the trend?
- 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.
- 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?
- 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?

**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.

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