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@ -13,8 +13,8 @@ linear model.
X 3 = Gender (1 for Female and 0 for Male), X 4 = Interaction between 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 GPA and IQ, and X 5 = Interaction between GPA and Gender. The
response is starting salary after graduation (in thousands of dollars). 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 = Suppose we use least squares to fit the model, and get β₀ = 50, β₁ =
20, β 2 = 0.07, β 3 = 35, β 4 = 0.01, β 5 = −10. 20, β₂ = 0.07, β₃ = 35, β₄ = 0.01, β₅ = −10.
(a) Which answer is correct, and why? (a) Which answer is correct, and why?
i. For a fixed value of IQ and GPA, males earn more on average i. For a fixed value of IQ and GPA, males earn more on average
@ -41,10 +41,10 @@ Suppose we use least squares to fit the model, and get β 0 = 50, β 1 =
4. I collect a set of data (n = 100 observations) containing a single 4. I collect a set of data (n = 100 observations) containing a single
predictor and a quantitative response. I then fit a linear regression 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 = 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 + . β₀ + β₁ X + β₂ X² + β₃ X³ + .
(a) Suppose that the true relationship between X and Y is linear, (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 i.e. Y = β₀ + β₁ X + . Consider the training residual sum of
squares (RSS) for the linear regression, and also the training squares (RSS) for the linear regression, and also the training
RSS for the cubic regression. Would we expect one to be lower 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 than the other, would we expect them to be the same, or is there