h2w answers added

hw2/answers

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+
+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 β  0 = 50, β  1 =
+20, β  2 = 0.07, β  3 = 35, β   4 = 0.01, β  5 = −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 =
+β 0 + β 1 X + β 2 X 2 + β 3 X 3 + .
+
+	(a) Suppose that the true relationship between X and Y is linear,
+	i.e. Y = β 0 + β 1 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.