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MATH2010 - Statistical Modelling I Coursework 2 This coursework accounts for 20...

May 7, 2024

Based on the provided context, the student is asking for help with a coursework assignment involving statistical modeling in R. The student needs to load data into R, fit a least-squares regression model, and perform model selection using AIC and BIC criteria. Here's how to approach the first question:

Explanation

The code defines a function to load training data and fit a least-squares regression model. It also includes a test function with two use cases to ensure the model fitting function works as expected.

Step-by-step Instruction

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Use the `lm` function in R to fit the model, specifying the formula and data

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Define concrete use cases and testing cases for the function: when user calls fit_least_squares() with a valid data path, it should return a fitted model object

Time Complexity

The time complexity is primarily dependent on the "lm" function, which typically runs in O(n^2 * p) time, where n is the number of observations and p is the number of predictors.

Space Complexity

The space complexity is O(n * p) due to the storage of the training data and the model coefficients.

Please note that the actual implementation of the model selection using AIC and BIC criteria would require additional code, which is not provided here due to the scope of the question.

For Task 1:

Key Concept

Least Squares Regression

Explanation

Least squares regression is used to fit a linear model by minimizing the sum of squares of the residuals.

For Task 2:

Key Concept

Model Selection

Explanation

Model selection using AIC and BIC helps in choosing a model that balances goodness of fit and model complexity.

For Task 3:

Key Concept

Predictive Model Selection

Explanation

The best predictive model is often the one with a good balance between accuracy and simplicity, avoiding overfitting.

For Task 4:

Key Concept

Lasso Regression

Explanation

Lasso regression is a type of linear regression that includes a penalty term to shrink coefficients towards zero to prevent overfitting.

For Task 5:

Key Concept

Cross-Validation

Explanation

Cross-validation is used to estimate the performance of the model on unseen data and to tune hyperparameters such as lambda in lasso regression.

For Task 6:

Key Concept

Variable Selection Comparison

Explanation

Comparing variable selection methods can reveal differences in model complexity and variable importance.

For Task 7:

Key Concept

Model Performance Evaluation

Explanation

The sum of squared errors (SSE) is a measure of model accuracy; the model with the lower SSE on test data is generally preferred.