Consider the data given in Table-1, and use the following Gradient Decent Methods to build the regression model: (a) BATCH METHOD (perform at least 3 iterations). Table-1 X 1 2 3 i 1 2 3 Y 1.5 2.0 2.5
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- MatLab Load the data flu.mat (you can do this by typing load flu in your script). This data is the flu trends seen in the United States 2005-2006, divided by region. We will use regressions to look at the data during flu season in the Pacific region. Create your x data: have x equal to 1:30. These represent 30 weeks between Oct. 2005 and May 2006. Create your y data: have y equal to flu.Pac(1:30)’. This is the flu trend for each week. Make sure you have an apostrophe after the last parenthesis. Fit the data below with a straight line and with a 2nd order polynomial. Use least-squares regression. Calculate the coefficient of determination (r^2) and the correlation coefficient (r) for each regression. Plot the two regression curves against the data. Which regression is better? Is there a polynomial you think would work better? Describe the data – what does it mean to you?In python, for a sample data with 4 columns and 60 rows how do you find the parameters for the regression with the feature map (see attached) where we consider the loss function to be the square of residuals. Once this is done, how do you compute the empirical risk? I've attached some of the data below, it would be sufficient to see how you get results for the question using the above dataset. 1 14 25 620 -1 69 29 625 0 83 27 850 0 28 25 1315 1 41 25 2120 -1 153 31 1315 0 55 25 2600 0 55 31 490 1 69 25 3110 1 83 25 3535The 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)
- You’ve just finished fitting a logistic regression model for email spam detection, and it is getting abnormally bad performance on both your training and validation sets (AUC of 0.55 on Train and 0.53 on Validation dataset). You know that your implementation has no bugs, so what could be causing the problem? a. You are underfitting b. You are overfitting.We use the Breast Cancer Wisconsin dataset from UCI machine learning repository: http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29 Data File: breast-cancer-wisconsin.data (class: 2 for benign, 4 for malignant) Data Metafile: breast-cancer-wisconsin.names Please implement this algorithm for logistic regression (i.e., to minimize the cross-entropy loss as discussed in class), and run it over the Breast Cancer Wisconsin dataset. Please randomly sample 80% of the training instances to train a classifier and then testing it on the remaining 20%. Ten such random data splits should be performed and the average over these 10 trials is used to estimate the generalization performance. You are expected to do the implementation all by yourself so you will gain a better understanding of the method. Please submit: (1) your source code (or Jupyter notebook file) that TA should be able to (compile and) run, and the…Implement a D-i-D in this problem. Load the dataset on STATA: use http://www.stata.com/data/jwooldridge/eacsap/jtrain1 This has data on firms and the amount of job training they get. Only use the data from 1987 and 1988. Carefully study the data before you proceed. Construct the D-i-D estimator in different ways: (a) Run the regressionhrsempit = β0 + β1 grant it + β21( year = 1988) + β3Ei + uit where Ei is a dummy variable for being a treatment (i.e. someone who would receive the grant in 1988). (b) Run the fixed effect regression with firm fixed effects θi: hrsempit = θi + β1 grant it + β21( year = 1988) + uit (c) Construct the 4 means of controls and treatments, before and after, and es- timate the difference in difference with means. (d) Do you get exactly the same answer, why or why not? (e) Now include other controls to estimate the D-i-D regression. Justify what- ever you include and interpret.
- implement a D-i-D in this problem. Load the dataset on STATA: use http://www.stata.com/data/jwooldridge/eacsap/jtrain1 This has data on firms and the amount of job training they get. Only use the data from 1987 and 1988. Carefully study the data before you proceed. Construct the D-i-D estimator in different ways: (a) Run the regressionhrsempit = β0 + β1 grant it + β21( year = 1988) + β3Ei + uit where Ei is a dummy variable for being a treatment (i.e. someone who would receive the grant in 1988). (b) Run the fixed effect regression with firm fixed effects θi: hrsempit = θi + β1 grant it + β21( year = 1988) + uit (c) Construct the 4 means of controls and treatments, before and after, and es- timate the difference in difference with means. (d) Do you get exactly the same answer, why or why not? (e) Now include other controls to estimate the D-i-D regression. Justify what- ever you include and interpret. Provide line by line code for STATA and the solutionTwo 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.I only need to use numpy library for this project I am not allowed any external library except panda and numpy. and work should be done in Jupyter notebook This project asks you to implement a logistic regression classifier, and apply it on a realdata set.We use the Breast Cancer Wisconsin dataset from UCI machine learning repository:http://archive.ics.uci.edu/ml/datasets/Breast+Cancer+Wisconsin+%28Diagnostic%29Data File: breast-cancer-wisconsin.data (class: 2 for benign, 4 for malignant)Data Metafile: breast-cancer-wisconsin.names we have seen that logistic regression is a convex problem, and gradientdescent gives the optimal parameters. However, the efficiency is highly dependent onthe step length which is left for users to tune. In this assignment, we look at a fastersolution called Newton’s method (a.k.a. Newton-Raphson method), which avoids theuse of step length. Please implement Newton-Raphson algorithm for logistic regression (i.e., to minimize the cross-entropy loss as…
- Write an order to generate binomial data with the number of observations (n) being 50, the number of trials (size) being 5 and the probability of success being 0.5, then storing the results in the binomial data matrix, with the number of columns being 5.Final output should be like sample runs shown in ques and attached images. Please solve.TODO 5 Use the Pandas DataFrame describe() method on our forestfire_df to get a statistical summary for each of our numerical features. # TODO 5.1ff_describe =display(ff_describe) todo_check([ (ff_describe.shape == (8, 11), 'ff_describe shape did not match (8, 11)'), (np.all(np.isclose(ff_describe.values[:4, 2:4].flatten(), np.array([517. , 517. , 90.64468085, 110.87234043,5.52011085, 64.04648225, 18.7 , 1.1 ]),rtol=.01)), 'The values of ff_describe were wrong!'),])