Applied Regression Analysis Categorical Predictors Homework Scientists wished to compare growth rates of two different types of bacteria. The growth was recorded at five equally spaced times for bacteria types A and B. The data will be in a data frame called bacteria after executing the following commands in R: GROWTH = c (8.0, 9.0, 9.1, 10.2, 10.4, 10.0, 10.3, 12.2, 12. 6, 13.9) TIME = rep (-2:2, 2) TYPE = factor (rep (c ("A", "B") , each = 5) ) bacteria = data . frame (TIME, GROWTH, TYPE) a. Construct a scatterplot of the data for the two types of bacteria using GROWTH as the response variable and TIME as the predictor variable. Distinguish between the observations from each group using different symbols and colors. Comment on what you see. b. Fit a one-way model for GROWTH using TYPE. What is the estimated mean growth for each group? c. Interpret all coefficients from b. in the context of the problem. d. Fit a main-effects model to GROWTH using TIME and TYPE. What is the estimated mean growth for each group? e. Interpret all coefficients from d. in the context of the problem. f. Fit an interaction model to GROWTH using TIME and TYPE. What is the estimated mean growth for each group? g. Interpret all coefficients from f. in the context of the problem. h. Compute the fitted line for the two types for the one-way, main effects, and interaction models (this will result in six lines). Plot these fitted lines in three separate plots of the scatterplot in a. i.e., plot the two fitted lines for each type for the one-way model in one plot, then the two fitted lines for each type for the main-effect model in a second plot, etc