In this part, you twill examine the hivariate relationships between the variables with a matrix of scatterplots and a correlation matrix {a} Obtain a matrix of scatterplots for The eightvariahles. Paste the mauix into your report Identify the pairs of variables exhibiting strong and moderate linear relationships {b} Obtain The correlation matrix for the eight variables. Paste the matrix into your report Using both matrices, comment on the relationship between nitrate concentration {EOE} and each of the seven predictors. It you wished to use only one explanatory variable to predict NOB, which variable would you choose? Is a linear model on the original scales appropriate for describing The relationship between NO3 and the seven predictors? Explain Now you will apply the natural logarithm transformation to each of the eight variables to make The relationship between the response variable {N03} and each explanamry variable approximately linear, reduce spread, and neutralize outliers. (a) Obtain a matrix of scatterplots for the eight log-nansfornred variables. Paste the matrix into your report Check the effectiveness of the tramformations by comparing to the matrix obtained in Question 2 and comment. Is a linear model on the log scales appropnlate for describing the relationship between NO3 and the seven predictors? [b] Obtain the correlation matrix for the eight log-transformed variables. Paste the matrix into your report Comment briey by relating to the analysis of Question 2, part (b) and Question 3, part {a}. Also, is collinearity an issue with this data? Define a multiple regression model with log-N03 as the response variable and the seven log transformed explaname variables. State The model assumptions. Use the backward elimination procedure to obtain the least squares r to The linear regression model dened in Question 4. (a) How many of the seven explanatory variables got eliminated by the backward elimination procedure? What is the order in which They were deleted? {b} 'What is the esdmated regression equation for the final model determined by the backward eliminaTion procedure? lMiat percentage of variation in log-NOB is explained by The explanatory variables in the model? (c) For the final model, is there evidence of any variable having an effect on mean logNO 3? State this question in terms of null and alternative hypotheses using the regression coefficients. Report the test statistic, The null distinction, and the pvalue. State your conclusion using c = 0.135. Moreover, comment on how each explanatory variable contributes individually, given the other variable{s] in the nal model and using c. = {3.05. In this part, you will obtain some diagnostic plots to verify the assumptions for the regression model obtained in the previous question. (a) Obtain a plot of residuals versus the fitted values for the nal model obtained in Question 5. Paste the plot into your report Is there evidence of non-constant variance or any outliers? Explain briey. {b} Obtain a normal probability plot of standardized residuals for the nal model obtained in Quesnion 5. Paste the plot into your report. Is there any evidence that the assumption of normality is violated? Comment briey