Please use R, provide R code if possible

1. 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.

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.

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.

Fit the model in (a) and provide the table of parameter estimates, standard

errors, etc.

d.

Write down the equation for the fitted regression line separately for each

species.

e.

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.

Does the common SD assumption seem reasonable in this setting? Justify

your response, considering this question both within and across species.

g.

Does the normality assumption seem reasonable in this setting? Justify your

response.

h.

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.

iii.

Specify the p-value.

iv.

Using a significance level of = 0.01, state your conclusions in the language

of the problem.

Below is data:

"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"

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"