Question 4 [14 marks] A team of zoologists is studying whether penguins living in captivity grow to reach their full adult height. The zoologists have selected a random sample of 95 adult penguins living in captivity. All of these penguins had been living in captivity since 6 months of age, though not all of them were born in captivity. Each penguin in the sample was given two types of growth supplement (type A and type B) at 6 months of age to promote normal growth. For each penguin, the following were recorded: adult height in metres [Y], amount of growth supplement A in grams (X1), amount of growth supplement B in grams 0(2) and whether the penguin was male or female {W = 1 if male and W = 0 if female]. A regression model was fitted to this data which produced the output displayed below. For the fitted model, the Festatistic and standard error of estimate were F = 382]] and 55 = 0,046. Predictor Coef SE Coef T pvalue Intercept 0.3684 0.0774 4.76 0.0000 X1 0.0249 0.0123 2.02 0.0458 X2 0.0042 0.0033 1.26 0.2108 W 0.2187 0.1112 1.97 0.0522 X] x W 0.0222 0.0184 1.21 0.2298 A. [1 mark] Write down the general form of the regression model that was fitted to this data. B. [2 marks] Test the overall significance of the model. Clearly state your hypotheses and use a significance level of 0! = 1%. C. [2 marks] Calculate the coefficient of determination for the fitted model. D. [2 marks] Test whether a different coefficient parameter for amount of growth supplement A is needed for female penguins. Clearly state your hypotheses and use a significance level of a = 10%. E. [3 marks] Test whether the intercept is less than 0.5. Clearly state your hypotheses and use a significance level of Ct = 5%. F. [4 marks] One of the zoologists believes that growth supplement B has a greater positive effect on adult height for penguins born in captivity than for penguins born in the wild. However, they are happy to assume that, for penguins that have not been given any growth supplement, there is no difference in expected adult height between penguins born in captivity or born in the wild. The zoologist would like to modify the initial regression model to help answer his question. Outline the process the zoologist needs to follow in order to test his belief. Explain all the required steps clearly, including the information the zoologist needs, the new model they need to fit (making sure to define any new variables) and the hypotheses they need to test {you do not need to conduct the test]