

1. Describe the null hypotheses to which the p-values given in Table 3.4
correspond. Explain what conclusions you can draw based on these
p-values. Your explanation should be phrased in terms of sales , TV ,
radio , and newspaper , rather than in terms of the coefficients of the
linear model.




3. Suppose we have a data set with five predictors, X 1 = GPA, X 2 = IQ,
X 3 = Gender (1 for Female and 0 for Male), X 4 = Interaction between
GPA and IQ, and X 5 = Interaction between GPA and Gender. The
response is starting salary after graduation (in thousands of dollars).
Suppose we use least squares to fit the model, and get β₀ = 50, β₁ =
20, β₂ = 0.07, β₃ = 35, β₄ = 0.01, β₅ = −10.

	(a) Which answer is correct, and why?
		i. For a fixed value of IQ and GPA, males earn more on average
		than females.

		ii. For a fixed value of IQ and GPA, females earn more on
		average than males.

		iii. For a fixed value of IQ and GPA, males earn more on average
		than females provided that the GPA is high enough.

		iv. For a fixed value of IQ and GPA, females earn more on
		average than males provided that the GPA is high enough.

	(b) Predict the salary of a female with IQ of 110 and a GPA of 4.0.

	(c) True or false: Since the coefficient for the GPA/IQ interaction
	term is very small, there is very little evidence of an interaction
	effect. Justify your answer.




4. I collect a set of data (n = 100 observations) containing a single
predictor and a quantitative response. I then fit a linear regression
model to the data, as well as a separate cubic regression, i.e. Y =
β₀ + β₁ X + β₂ X² + β₃ X³ + .

	(a) Suppose that the true relationship between X and Y is linear,
	i.e. Y = β₀ + β₁ X + . Consider the training residual sum of
	squares (RSS) for the linear regression, and also the training
	RSS for the cubic regression. Would we expect one to be lower
	than the other, would we expect them to be the same, or is there
	not enough information to tell? Justify your answer.

	(b) Answer (a) using test rather than training RSS.

	(c) Suppose that the true relationship between X and Y is not linear,
	but we don’t know how far it is from linear. Consider the training
	RSS for the linear regression, and also the training RSS for the
	cubic regression. Would we expect one to be lower than the
	other, would we expect them to be the same, or is there not
	enough information to tell? Justify your answer.
	(d) Answer (c) using test rather than training RSS.