- Rating X1 64 4 73 4 61 4 76 4 72 6 80 6 71 6 83 6 83 8 89 8 86 8 93 8 88 10 95 10 94 10 100 10 X2 Not Sweet Sweet Not S 1 (68.57 KiB) Viewed 115 times
- Rating X1 64 4 73 4 61 4 76 4 72 6 80 6 71 6 83 6 83 8 89 8 86 8 93 8 88 10 95 10 94 10 100 10 X2 Not Sweet Sweet Not S 2 (75.16 KiB) Viewed 115 times
Unless otherwise stated, carry out inferences using a = 0.05. Hypotheses should be written in terms of parameters when possible, and conclusions of hypothesis tests should be given using the context of the problem. Recall the cake preference data set discussed in class. The response variable is a preference score, where a high number represents high preference. Cake moisture content is recorded as the continuous variable X1, while X, can be treated as a binary categorical variable recorded as "sweet" or "not sweet." The 16 observations are housed in the file cake_ratings.txt. a) To ensure all the data have been read in, reproduce the mean of the response variable as Y = 81.75. b) Suppose we wish to fit an ANCOVA model using these two predictors. State the ANCOVA model using mathematical symbols. c) We would like to visualize whether there is a linear relationship between moisture content and cake rating at each level of sweetness. Produce one or more separate scatter plots that include two regression lines, one for each sweetness category. d) Use the appearance of the plots above to explain whether the ANCOVA model seems appropriate. e) Use Minitab to fit the ANCOVA model. Provide a table of output that will permit you to execute the overall F-test. f) Give numeric evidence of the degree to which this ANCOVA model fits the data. Is the fit particularly good/bad?