Suppose that the following data were obtained by an investigator studying the influence of estrogen injections on change in the pulse rate of adolescent chimpanzees:

a. What are the factors in this experiment? Should they be designated as fixed or random?
b. Demonstrate that the cell frequencies for two-way ANOVA in this problem are proportional; that is, nij = ni.n.J/n.. for each of the four cells.
c. Use the following table of sample means

and the general formulas

to analyze the data for this problem, employing the usual methodology for equal-cell-number two-way ANOVA and the fact that SSE = 530.24078 (i.e., compute the sums of squares for rows, columns, and cells directly, and then obtain the sum of squares for interaction by subtraction).
d. What regression model is appropriate for analyzing this data set?
e. Using the regression analysis results given in the following table, check whether SS(Rows) = Regression SS(SEX) = Regression SS(SEX|TREATMENT) and SS(Columns) = Regression SS(TREATMENT) = Regression SS(TREATMENT|SEX), where SS(Rows) and SS(Columns) are as obtained in part (c). What has been demonstrated here?

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Control: 5.1,-2.3,4.2, 3.8, 3.2,-15, 6.1,-2.5, 1.9.-3.0,-2.8,1.7 Ee15.0, 62, 4.1, 2.3,7.6, 14.8, 12.3, 13.1.34,8.5, 112, 69 Male Control: 2.3,-5.8,3.8, 5.5, 1.6,-2.4,1.9 Estrogen: 7.3, 2.4,6.5, 8. 10.3, 2.2, 12.7, 6.3 Female Sex Control Estrogen Male Female 1.158333 0.100000 8.783333 6.975000 SS(columns)-Σ n.,(Kr-Y )2 Source d.f SEX TREATMENT SEX SEX × TREATMENT | SEX, TREATMENT Residual 19.72667 536.55619 135000 550.24078 36 Source d.f TREATMENT 536.5561 SEX X TREATMENTJSEX, TREATMENT Residual 19.72667 135000 30.24078 36 ieniTREATMENTm -1 ifcontnol SEX l if female nd TREATMENT I if estrogen