The data set plant is from a factorial experiment on the effects of CO2 concentration (ambient vs. high) and soil temperature (low vs. high) on plant growth in 12 environmentally controlled chambers. The four treatment combinations were randomly assigned to the chambers ( 3 chambers per treatment combination), and 12 plants were grown in each chamber. The variable plant.wt gives the mean accumulated dry weights for the 12 plants in each chamber. This experiment was actually run on three plant species simultaneously. For this problem, use only the data for needlegrass (species 2). DATA set plant: One way to extract data for species 2 : (a) Draw a graph of the plant weights in the four combinations of CO2 and temperature and describe the patterns you see. (b) Perform an analysis of variance of plant weight, using a model that includes co2, temp, and their interaction. Include (i) a summary of the mean response in the different treatment combinations; (ii) the ANOVA table; and (iii) an interpretation of your results. Note: For this part, use ANOVA, rather than regression, output. There is not an exact correspondence between the P-values in the regression output and those in the ANOVA output, as explained in the lecture notes. (c) Use Levene's test to evaluate the constant-variance assumption of your ANOVA model. Is the result consistent with what you see in your graph from part (a)? Explain. (d) Since the interaction term is nonsignificant, drop it and fit a model with just the main effects of CO2 and temperature. Present both the ANOVA and regression output, and explain what they suggest about the effects of CO2 and temperature on plant weight. (e) Using the ANOVA output from the two models you fit above, do an extra-sum- ofsquares test of the null hypothesis that there is no interactive effect of CO2 and temperature on plant growth. That is, extract the needed sums of squares and degrees of freedom, and plug them in to the general formula for the extra-sum-of-squares Ftest. Show how to obtain the P-value and verify that it is the same as that for the interaction term in the full model from part (b)