The tuna fish data from Exercise 11.16 were analyzed as a completely randomized design with four treatments. However, we could also view the experimental design as a 2 × 2 factorial experiment with unequal replications. The data are shown below.9

The data can be analyzed using the model
y = β0 + β1x1 + β2x2 + β3x1x2 + ε
where
x1 = 0 if oil, 1 if water
x2 = 0 if light tuna, 1 if white tuna
a. Show how you would enter the data into a computer spreadsheet, entering the data into columns for y, x1, x2, and x1x2.
b. The printout generated by MINITAB is shown below. What is the least-squares prediction equation?
MINITAB output for Exercise 13.32
Regression Analysis: y versus x1, x2, x1x2
The regression equation is
y = 1.15 - 0.251 x1 + 0.078 x2 + 0.306 x1x2
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c. Is there an interaction between type of tuna and type of packing liquid?
d. Which, if any, of the main effects (type of tuna and type of packing liquid) contribute significant information for the prediction of y?
e. How well does the model fit the data? Explain.

Oil Water Light Tuna 1.92 1.23 0 White Tuna 1.27 1.22 1.27 1.28 1.22 Predictor Constant xl x2 x1x2 Coef 1.1473 -0.2508 0.0777 0.3058 SE Coef 0.1370 0.1830 0.2652 0.3330 0.000 0.180 9.39 0.29 0.92 0.365 S 0.454287 R-Sq ( adj ) 3.98 Analysis of Variance DF Source Regression Residual Error Total MS 3 0.9223 0.304 1.49 0.235 33 6.8104 0.2064 36 7.7328