In the statistical model in Equation (4.5), the following assumptions need to be validated about the random error terms, ijk, before any formal hypothesis test

In the statistical model in Equation (4.5), the following assumptions need to be validated about the random error terms, ɛijk, before any formal hypothesis test can be developed:
• The error terms are independent and identically distributed.
• The error terms follow a normal probability distribution, denoted as ɛ ̴ N(0, σ2).
the second assumption includes an equal variance assumption about the random errors from the different factor- level groups: σ112 = σ122 = σ132 = σ212 = σ222 = σ232.
a. The independence assumption implies that there is no relationship between one observation and the next. The identically distributed assumption means that each observation sampled within each brand/ water combination is from a population with the same mean and variance. If all 26 paper towels were sampled from one roll to assess the Brand C/5 drops factor combination, would you be concerned about violating the independence and/or the identically distributed assumption? Why or why not?
b. Calculate the sample means and standard deviations of all six factor- level combinations. Clearly, some groups have much larger variation than others. In addition, the variation within each group increases as the average breaking strength increases. To address this issue, a transformation of the data can often be used that will “ stabilize” the variances so that the equal variance assumption is reasonable on this new scale. (Chapter 2 describes transformations in more detail.)
c. Transform the response variable using natural log (Strength) and √Strength. Did both trans-formations improve the equal variance assumption?