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3. As part of an investigation of toxic agents, 48 rats were allocated to 3 poisons (I,II,III) and 4 treatments (A,B,C,D). The response was survival time in tens of hours. The data is in rats.csv. (a) Read the data into R and compute the cell means. (b) Construct an interaction plot to display the mean responses for each combination of the two factors. Which poison appears most toxic? Does there appear to be a difference in the average survival times for different treatments? (c) Perform a two-way ANOVA with interaction. State the equation of such a model. Is the interaction significant? Explain the relevant hypothesis and discuss your conclu- sion with reference to your interaction plot. (d) Find the fitted and the residual value for the last observation in the dataset. (e) Are the main effects significant? Test as appropriate and interpret. Note: state the hypotheses, test statistics and p-values. Find the appropriate critical values for the F test at a 0.05. (f) Which treatment (treat) would you recommend? Check confidence intervals for each pairwise difference between treatment means. (g) For the model with no interaction, check the model assumptions using residual plots. 3. As part of an investigation of toxic agents, 48 rats were allocated to 3 poisons (I,II,III) and 4 treatments (A,B,C,D). The response was survival time in tens of hours. The data is in rats.csv. (a) Read the data into R and compute the cell means. (b) Construct an interaction plot to display the mean responses for each combination of the two factors. Which poison appears most toxic? Does there appear to be a difference in the average survival times for different treatments? (c) Perform a two-way ANOVA with interaction. State the equation of such a model. Is the interaction significant? Explain the relevant hypothesis and discuss your conclu- sion with reference to your interaction plot. (d) Find the fitted and the residual value for the last observation in the dataset. (e) Are the main effects significant? Test as appropriate and interpret. Note: state the hypotheses, test statistics and p-values. Find the appropriate critical values for the F test at a 0.05. (f) Which treatment (treat) would you recommend? Check confidence intervals for each pairwise difference between treatment means. (g) For the model with no interaction, check the model assumptions using residual plots.