FITTING A REGRESSION LINESYou have been provided with a data file which has data on wheat production in Australia over the last four decades of the twentieth century (FAOSTAT Australia WheatProd.csv ).The data are extracted from the FAOSTAT database and include information on the following variables: production areas in hectares (“area”), output in tonnes (“production”), yield in hectograms per hectare (“yield.hgha”), and a time tend variable (“time”). Investigate if yield levels are related to time and the nature of any such relationship. Conduct a structured investigation of this theory using the data available. Results for this question should be presented in the form of a report similar to the sample that was posted with the assignment in the LMS. The key results to include in the report should address the following requirements, and the results indicated below.(a) A description of the data set using a summary table (including means, medians, standard deviaitons, etc.)(b) An appropriate graphical representation of the data.(c) A formal statement of a null hypothesis.(d) Results from a simple regression equation relating wheat yield to time, with a summary and interpretation of the results.(e) A discussion of whether the linear functional form is appropriate for describing the relationship between yield and time.(f) Results from a second regression where observations with numerically big residuals (oroutliers) are removed. For this purpose, we will dene outliers simply to be observations for which therst regression model under- or over-estimated yield by more that 40% of the mean yield for the sample. In your report, state what observations were removed asa result of applying this rule. Describe how the regression results change.(g) Use the model estimated without outliers to predict expected wheat yields for the years 2025 and 2050. Provide the 95% condence intervals for the yield predictions.(h) Plot the data, the two estimated regression equaltions and the yield prediction intervals for 2025 and 2050 (all in one plot). Include the plot in your report. Use legends and colours to identify the regression plots.
