Assignment Task
Question 1 – Linear Regression
In this question, you need to implement a linear regression model to predict the residuary resistance of sailing yachts. The data set used in this question can be found in ‘yacht_hydrodynamics.csv.’ The data set has 7 features, which are summarized as below.
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Get Help Now!Variations concern hull geometry coefficients and the Froude number:
- Longitudinal position of the center of buoyancy, adimensional.
- Prismatic coefficient, adimensional.
- Length-displacement ratio, adimensional.
- Beam-draught ratio, adimensional.
- Length-beam ratio, adimensional.
- Froude number, adimensional.
The measured variable is the residuary resistance per unit weight of displacement:
- Residuary resistance per unit weight of displacement, adimensional.
Specifically, you need to:
- Perform data pre-processing, including removing invalid data, transforming the categorical features to numerical features or other operations if necessary. (4 marks)
- Split the data set into a training set and a test set, with the ratio of 8:2. (1 mark)
- Implement stochastic gradient descent to train a linear regression model with your training data. Visualize the parameter updating process, test error (RMSE) in each iteration, and cost convergence process. Please be advised that built-in models in any released R package, like glm, are NOT allowed to use in this question. You can choose your preferred learning rate and determine the best iteration number. (8 marks)
- Evaluate your model by calculating the RMSE, and visualizing the residuals of test data. Please note that an explanation of your residual plot is needed. (5 marks)
- Does your model overfit? Which features do you think are not significant? Please justify your answers. For example, you can analyze the significance of a feature from correlation, variance, etc. (8 marks)
- Use the glmnet library to built two linear regression models with Lasso and Ridge regularization, respectively. In comparison to your model, how well do these two models perform? Do the regularized models automatically filter out the less significant features? What are the differences between these two models? Please justify your answers. (8 marks
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