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 4, Problem 8E
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Method for classification
- In the case of KNN with K=1, there is a training error rate of 0% because in this case,
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Theoretical Overview
Suppose we have a set of data consisting of ordered pairs and we suspect the x and y coordinates are related. It is natural to try to find the best line that fits the data points. If we can find this line, then we can use it to make all sorts of other predictions. In this project, we're going to use several functions to find this line using a technique called least squares regression. The result will be what we call the least squares regression line (or LSRL for short).
In order to do this, you'll need to program a statistical computation called the correlation coefficient, denoted by r in statistical symbols:
NOTE: Equation is written assuming you start at the value 1. Lists start at index 0.
Once you have the correlation coefficient, you use it along with the sample means and sample standard deviations of the x and y-coordinates to compute the slope and y-intercept of your regression line via these formulas:
Tasks:
In this project, you must read…
You run a logistic regression model in R using the glm() function. The dependent variable is the factor
variable Y and independent variables are X1 and X2 (in other words, the formula is Y~X1+X2). In the
model output, the coefficient of the constant term is a0, the coefficient of X1 is a1, and the
coefficient of X2 is a2. Assuming a cutoff = 0.5, which of the following defines the equation of a
decision boundary?
a0 + a1X1 + a2X2 = 0.5
exp(-(a0 + a1X1 + a2X2)) = 0
a0 + a1X1 + a2X2 = 0
O exp(-(a0 + a1X1 + a2X2)) = 0.5
I need to plot the data from a simple linear regression with its values x and y with the fitted y values from fitting a logistic regression model. How do I plot the x values with two different y's, y values on the left side with fitted y values on the right? I want to generate the fitted/predicted y values using logistic regression and then create a plot using all those three variables? Here is an example of my SAS code that doesn't work.
data coupons;input redeemed discount;cards;100 5147 9176 11211 13244 15277 17310 19343 21;run;
ods graphics on;proc logistic data=coupons;model redeemed(event='1') = discount;effectplot;run;
It give me this warnings and I do not understand….
NOTE: Option EVENT= is ignored since LINK=CLOGIT.
NOTE: PROC LOGISTIC is fitting the cumulative logit model. The probabilities modeled are summed over the responses having the lower
Ordered Values in the Response Profile table. Use the response variable option DESCENDING if you want to reverse the
assignment of…
Chapter 4 Solutions
An Introduction to Statistical Learning: with Applications in R (Springer Texts in Statistics)
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- Implement a simple linear regression model using Python without using any machine learning libraries like scikit-learn. Your model should take a dataset of input features X and corresponding target values y, and it should output the coefficients w and b for the linear equation y =wX + barrow_forwardThe ols() method in statsmodels is used to fit a simple linear regression model using “Exam4” as the response variable and “Exam3” as the predictor variable. The output is shown below. A text version is available. What is the correct regression equation based on this output? Is this model statistically significant at 10% level of significance (alpha = 0.10)? Select one. (Hint: Review results of F-statistic)arrow_forwardWrite a python program to implement Linear Regression algorithm. Use the sample data-set [(1,3) (2,5) (3,7) (4,7) (5,11) (6,13)] to predict the values for X=10, 15, 20, 25. Evaluate the accuracy of the model (R2 value).arrow_forward
- Imagine a regression model on a single feature, defined by the function f (x) = wx + b where X, W, and b are scalars. We will use the MSE loss loss(w, b) = E;(f(x;) – t;)² . n Work out the gradient with respect to b. Which is the correct answer? Read the four equations carefully, so you notice all the differences. 1. E:(f(x;) – t;)x; 2.E(f(x;) – t;) n 3.- E;(wx; + b – t;)x; n 4. E: (wa; +b - t;) n 4arrow_forwardA group of researchers conducted a study to investigate the effectiveness of a new teaching method for a particular subject. They randomly assigned 100 students to two groups: one group received the new teaching method, and the other group received the traditional teaching method. At the end of the semester, they measured the students' performance on a standardized test. The researchers found that the mean score for the group that received the new teaching method was higher than the mean score for the group that received the traditional teaching method. How can the researchers test the hypothesis that the new teaching method is more effective than the traditional teaching method? What statistical test should they use?arrow_forwardWrite a computer code to do linear regression analysis of a given dataset to find the relation between two variables which gives the least sum of squares error. Using Excel or Matlab. Include a copy of the script, a sample input, and a sample output from your codes. Sample output must include modelfit parameters and the sum of the squared errors for the fit. Please also run the code for thefollowing data set to find and report the relation between y and x:x y25 3040 80120 15075 80150 200300 350270 240400 320450 470575 583arrow_forward
- Write code to define a K-NN regression model with K=5 and the neighbors are weighted by the inverse of their distance. [ ] # Write your code herearrow_forwardNow suppose that you have two versions of your model with different parameters(e.g., different regularization) or even different model families (e.g., logistic regression versus random forest). Which one is better?arrow_forwardWhat are Ensemble Algorithms? Write an algorithm for BOOSTING method. Assume that two individuals offer to sell you their predictive models M1 and M2. The confusion matrices produced by each model are as follows. What is the accuracy of each model? Assuming that precision is of paramount importance in your application, which of the two models would you buy? Why? Performance of M1 Performance of M2 Predicted True Predicted False Predicted True Predicted False Actually True 5 95 Actually True 85 15 Actually False 10 90 Actually False 95 5arrow_forward
- Two engineers were independently testing a cubic polynomial regression model on the same dataset. The first engineer used the validation set approach, while the second one used 10-fold cross-validation to estimate test MSE. Both of them repeated the test 20 times, each time with a different set.seed() number. Then, each engineer calculated the mean and the standard deviation of his 20 estimated test MSE. Which of the following statement is most likely true? • The standard deviation of MSE from the first engineer will be greater than the standard deviation of MSE from the second engineer. • The mean MSE from the first engineer will be less than the mean MSE from the second engineer. • The mean MSE from the first engineer will be greater than the mean MSE from the second engineer. • The standard deviation of MSE from the first engineer will be less than the standard deviation of MSE from the second engineer.arrow_forwardIn linear regression, 8 tells us how meaningful the corresponding x is in predicting the output. This means, ...... O if a particular 8-value is very small compared to others, the corresponding x plays a little role in predicting the output. O if a particular 8-value is very large compared to others, the corresponding x plays a little role in predicting the output.arrow_forward2. Can you design a binary classification experiment with 100 total population (TP+TN+FP+ FN), with precision (TP/(TP+FP)) of 1/2, with sensitivity (TP/(TP+FN)) of 2/3, and specificity (TN/(FP+TN)) of 3/5? (Please consider the population to consist of 100 individuals.)arrow_forward
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