An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
13th Edition
ISBN: 9781461471370
Author: Gareth James
Publisher: SPRINGER NATURE CUSTOMER SERVICE
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Chapter 3, Problem 6E
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Linear regression
- The least square line equation is
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For logistic regression, the gradient of the cost function is given by J(0) =
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In R, write a function that produces plots of statistical power versus sample size for simple linear regression. The function should be of the form LinRegPower(N,B,A,sd,nrep), where N is a vector/list of sample sizes, B is the true slope, A is the true intercept, sd is the true standard deviation of the residuals, and nrep is the number of simulation replicates. The function should conduct simulations and then produce a plot of statistical power versus the sample sizes in N for the hypothesis test of whether the slope is different than zero. B and A can be vectors/lists of equal length. In this case, the plot should have separate lines for each pair of A and B values (A[1] with B[1], A[2] with B[2], etc). The function should produce an informative error message if A and B are not the same length. It should also give an informative error message if N only has a single value. Demonstrate your function with some sample plots. Find some cases where power varies from close to zero to near…
please show step by step working, if python code can be provided, it will be good!
Chapter 3 Solutions
An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
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- Implement the Linear regression for given one independent variable. (using jupyter notebook) thanks a lot in advance:)arrow_forwardWe are interested in estimating the total BEEF consumption per person given BEEF and POPULATION totals for n countries. One obvious way to estimate this is using a ratio estimator with y = BEEF and x = POPULATION. How can a linear regression estimator, Hansen-Hurwitz and Horwitz-Thompson estimator be used to do this?arrow_forwardWhy don't we use the ordinary least square to learn a linear regression model for a classification problem (i.e., learning to fit the label of 0 or 1)? Select one: a. Linear regression cannot output value in a probability range. b. OSL will learn a bad linear regression model for a classification. c. Yes, we can. Linear regression is the same as logistic regression. d. Linear regression outputs continuous variable.arrow_forward
- We create a simple regression model and call the fit function as follows: Im=LinearRegression() Im.fit(X,Y) in a multilinear model we proceed in the same way: mlm=LinearRegression() mlm.fit(Z,Y) How does the linear regression model knows if we are doing a simple or multiple linear regression? Answer:arrow_forwardConsider 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.arrow_forwardANSWER ALL QUESTIONSarrow_forward
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