4. [30 pts] Researchers wanted to identify factors associated with agricultural intensity. After sampling 29 different regions, they collected the following variables Agricultural intensity Population density (people per km) Livestock indicator (is livestock present? 1- yes 0-no). Mean precipitation (average rainfall) (in mm per year) To assess the factors, the researchers chose regression. After fitting the model once, they decided to log transform agricultural intensity. Below is the output from their analysis after the log transform (using log agricultural density). Use the output below to answer the following questions. Stata Output: regress logagintensity popdens livestock meanprecip Source SS df MS Number of obs 29 F(3, 25) 17.13 Model Residual 3.26163452 1.58694335 3 1.08721151 25 .063477734 Prob > F 0.0000 R-squared 0.6727 Adj R-squared 0.6334 Total 4.84857786 28 .173163495 Root MSE .25195 logaginten-y Coef. Std. Err. t P>Itl [95% Conf. Interval] popdens .0039553 livestock .1385403 .0008642 .1070604 meanprecip -.0001762 cons 1.446662 .0000631 .1609116 4.58 0.000 1.29 0.207 -2.79 0.010 .0021755 .0057352 -.0819548 3590353 8.99 0.000 -.0003061 1.115258 -.0000464 1.778065 Questions: 4a) [8 points] What are the key assumptions of linear regression? 4b) [10 points] Assuming all the assumptions named in 4a) hold, is the model significant (yes or no)? State the null and alternative hypotheses and state the test statistic value and p-value for the model. (We will postpone interpreting the model, focusing on specific questions later) 4c) [5 points] Provide the R2 and interpret it. Styles 4d) [7 points] Assuming the model presented is the best model, how would we report the effect of population density on agriculture intensity? (i.e., how would we interpret the coefficient of population density?) I