Comparative Regression Modelling Analysis

00:00 10 marks

A dataset with 50 observations is provided containing a response variable and three predictor variables. Investigate how polynomial, logistic, and trigonometric regression models can be used to model the data. Discuss the methodology for multi-regression analysis using technology and compare the models based on the sum of squared errors (SSE).

You are required to:

(a) Gather and preprocess the data, including generating scatter plots and summary statistics.

(b) Use technology to compute and compare the SSE for each model, and explain which model best fits the data.

Part a

8 minutes 4 marks

Question

Describe the steps you would take to gather and preprocess the dataset for regression analysis. Include methods for identifying outliers, handling missing values, and generating scatter plots as well as summary statistics.

Hint Hint

Hint

Consider data cleaning, visualization, and computation of basic statistics in your approach.

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Complete Answer

Step 1: Inspect the dataset for missing values and outliers, and decide whether to impute or remove problematic data. Step 2: Generate scatter plots for the response variable against each predictor to visually assess relationships. Step 3: Compute summary statistics (e.g., mean, median, standard deviation) for each variable to understand the distribution.

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Part b

7 minutes 6 marks

Question

Using technology, compute the Sum of Squared Errors (SSE) for the polynomial, logistic, and trigonometric regression models. Explain which model best fits the data based on the SSE values and justify your choice.

Hint Hint

Hint

Recall that the model with the lowest SSE is preferred because it indicates a closer fit to the data.

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Complete Answer

After computing the SSE for each regression model, the model with the smallest SSE is deemed the best. For example, if the polynomial model yields an SSE of 130, logistic 145, and trigonometric 115, then the trigonometric regression model best fits the data because 115 is the lowest value.

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