(19 marks) A random sample of irises of three different species (A, B, and C) from a particular region was collected. The length and width of one petal on each flower were recorded, along with its species. The data are available in the file flower.txt. Of interest is the linear relationship between mean petal length and petal width, and how this relationship differs across species. You may assume that petal lengths are independent.

a. (2 marks) Write down the linear model for these data using regression notation for all predictors. Be sure to define your variables and to state all assumptions.

b. (2 marks) Write down the linear model for these data using regression notation for numeric predictors and ANOVA notation for categorical predictors. Be sure to define your variables and to state all assumptions.

c. (1 mark) Fit the model in (a) and provide the table of parameter estimates, standard errors, etc.

d. (2 marks) Write down the equation for the fitted regression line separately for each species.

e. (2 marks) Produce a scatterplot to illustrate the relationship between petal length and width, using a different colour for each species. Be sure to label the axes appropriately. Include the fitted regression lines.

f. (3 marks) Does the common SD assumption seem reasonable in this setting? Justify your response, considering this question both within and across species.

g. (2 marks) Does the normality assumption seem reasonable in this setting? Justify your response.

h. (5 marks) Conduct the test of whether the slopes of the regression lines vary across species.

In particular:

i. Specify the null and alternative hypotheses.

ii. Specify the value of the test statistic.

"Length" "Width" "Species" 1. 22 0. 132 "A" 1. 32 0. 198 "A" 1. 25 0. 556 "A" 1. 08 0. 258 "A" 1. 58 0.27 "A" 1. 79 0. 587 "A" 1. 53 0. 336 "A" 1. 67 -0 . 009 "A" 2. 14 0. 107 "A" 1. 24 0. 155 "A" 0 . 75 0. 489 "A" 1. 86 0. 316 "A" 1. 24 0 . 324 "A" 1. 22 0. 266 "A" 1. 78 0.133 "A" 1. 53 0. 601 "A" 1. 07 0.344 "A" 1.33 -0.149 "A" 1. 48 0.384 "A" 1. 42 0.149 "A" 1. 49 0.03 "A" 1.3 0.2 "A" 1. 59 0. 039 "A" 3.9 1. 18 "B" 4. 14 1. 201 "B" 4. 02 0. 989 "B" 4. 72 1. 494 "B" 4. 19 1. 357 "B" 4. 24 1. 098 "B" 5. 08 1. 577 "B" 4. 61 1. 411 "B" 4. 23 1. 267 "B" 4. 36 1. 505 "B" 5. 07 1. 502 "B" 4. 34 1. 49 "B" 5.3 1. 464 "B" 5. 01 1. 437 "B" 4. 14 1. 314 "B" 3. 77 1.265 "B" 3. 85 1. 25 "B" 5. 55 1. 887 "C" 5. 43 1. 984 "C" 5 . 26 1. 773 "C" O E M3.9 1. 18 "B" 4. 14 1. 201 "B" 4. 02 0. 989 "B" 4. 72 1.494 "B" 4. 19 1. 357 "B" 4. 24 1. 098 "B" 5. 08 1.577 "B" 4. 61 1. 411 "B" 4. 23 1. 267 "B" 4.36 1.505 "B" 5. 07 1. 502 "B" 4. 34 1.49 "B" 5.3 1. 464 "B" 5. 01 1. 437 "B" 4. 14 1.314 "B" 3.77 1. 265 "B" 3. 85 1. 25 "B" 5. 55 1. 887 "C" 5. 43 1. 984 "C" 5. 26 1. 773 "C" 5. 48 2. 46 "C" 5. 69 2. 268 "C" 5. 12 1. 801 "C" 4. 89 1. 945 "C" 5. 35 1. 933 "C" 5. 98 2. 182 "C" 5. 33 2. 009 "C" 5. 8 2. 077 "C" 4. 96 2. 02 "C" 5. 52 2. 017 "C" 5 . 91 2.3 "C" 5. 63 1. 981 "C" 5. 78 2. 329 "C" 5. 12 1. 716 "C" 5. 32 2. 143 "C" 5. 19 2 . 051 "C" 5. 62 2. 069 "C" 5 . 25 2. 102 "C"