Problem 3.4
A a set of data (n = 100 observations) has been collected containing a single
predictor and a quantitative response. A  linear regression model has been fitted to the data, as well as a separate cubic regression, i.e.
y = β0 + β₁x + β₂x² + β₃x³ + ε.
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(a) Suppose that the true relationship between x and y is linear, i.e. y = β₀ + β₁X + ε. 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.
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