An introduction to statistical learning: with applications in R
An introduction to statistical learning: with applications in R
13th Edition
ISBN: 9781461471387
Author: James, Gareth, Witten, Daniela, Hastie, Trevor, TIBSHIRANI, Robert
Publisher: MPS (CC)
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Chapter 3, Problem 11E

a.

Explanation of Solution

Simple linear regression

  • A simple linear regression is performed on y onto x without an intercept...

b.

Explanation of Solution

Simple linear regression

  • A simple linear regression is performed on y onto x without an intercept...

c.

Explanation of Solution

Simple linear regression

  • The same value is obtained for the t-statistic and consequently the same value for the corresponding p-value...

d.

Explanation of Solution

Simple linear regression

  • The regression of Y onto X without an intercept.
  • Hence the result is verified numerically...

e.

Explanation of Solution

Simple linear regression

  • It is easy to see that if xi is replac...

f.

Explanation of Solution

Simple linear regression

  • Here the regression is performed with an intercept...

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Consider a linear regression setting. Given a model's weights W E RD, we incorporate regularisation into the loss function by adding an la regularisation function of the form-W;|*. Select all true statements from below. a. When q = 1, a solution to this problem tends to be sparse. I.e., most weights are driven to zero with only a few weights that are not close to zero. b. When q = 2, a solution to this problem tends to be sparse. I.e., most weights are driven to zero with only a few weights that are not close to zero. c. When q = 1, the problem can be solved analytically as in closed form. d. When q = 2, the problem can be solved analytically as in closed form.
For logistic regression, the gradient of the cost function is given by J(0) = (i) E (he (x) – y')x;). Write down mathematical expression(s) for the correct m gradient descent update for logistic regression with a learning rate of a. (In the expression, he(x^) should be replaced by the sigmoid function.)
in a trained a logistic regression classifier. it outputs a new example x with a prediction ho(x) = 0.3. This means: Select one: Oa. Our estimate for P(y-1 | x) Ob. Our estimate for Ply-0 | x) Oc. Our estimate for P(y-1 | x) Od. Our estimate for P(y=0 | x)
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