From b77210065143704dffadf35549c4ff5a501436a5 Mon Sep 17 00:00:00 2001 From: caes Date: Mon, 30 Jan 2017 01:45:45 -0500 Subject: [PATCH] h2w answers added --- hw2/answers | 61 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 61 insertions(+) create mode 100644 hw2/answers diff --git a/hw2/answers b/hw2/answers new file mode 100644 index 0000000..03cf735 --- /dev/null +++ b/hw2/answers @@ -0,0 +1,61 @@ + + +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. \ No newline at end of file