Module Assignment: Module 4 QMB-6304 Analytical Methods For ✓ Solved

Module Assignment Module 4 QMB-6304 Analytical Methods for Business Write a simple R script to execute the following

Load the data from “Assignment 4 Data.xlsx” into R, which contains age, weight, and height for 251 adults. Create a new variable for each individual’s body mass index (BMI) using the formula BMI = (weight0.45) / (height0.025)^2. From this master dataset, take a random sample of 45 cases using the numerical portion of your U number as the seed. Conduct a simple linear regression with weight as the independent variable and BMI as the dependent variable, and report the beta coefficients, p-values, and confidence intervals. Provide a written interpretation of the beta coefficients. Assess whether the model meets the assumptions of linear regression. Using the model, predict the BMI for an individual weighing 185 pounds, including 95% confidence and prediction intervals with interpretations. Explain two reasons why it would be inappropriate to use this model to predict a 10-year-old boy’s BMI who weighs 72 pounds. Include the R script and results in a single MS-Word file.

Sample Paper For Above instruction

Introduction

The objective of this analysis is to develop a linear regression model that predicts Body Mass Index (BMI) based on weight among adults, utilizing a dataset containing age, weight, and height. The process involves data preprocessing, sampling, model fitting, interpretation, and validation, culminating in predictive application and evaluation of the model's appropriateness for different populations.

Data Loading and Preparation

The dataset, "Assignment 4 Data.xlsx," was imported into R using the "readxl" package. The dataset comprised 251 observations of adults, each with recorded age, weight (in pounds), and height (in inches). To compute BMI, a new variable was created, applying the provided formula:

BMI = (weight 0.45) / (height 0.025)^2

This transformation converted weight to a metric equivalent and height to meters, aligning with standard BMI calculations. The addition of the BMI variable enabled subsequent analysis on the relationship between weight and BMI.

Sampling

Using R's set.seed() function with a seed number derived from the user's U-number, a random sample of 45 observations was selected from the master dataset. This sampling method ensured reproducibility. The sampled data served as the primary dataset for the regression analysis, providing a manageable subset that still reflects the broader population's characteristics.

Regression Analysis

A simple linear regression was performed using the "lm()" function with BMI as the dependent variable and weight as the independent variable. The model output indicated significant results, with the estimated beta coefficient for weight, its standard error, p-value, and confidence interval reported.

The coefficient estimate suggests that for each additional pound of weight, BMI increases by approximately [value] units, holding other factors constant. The p-value associated with this coefficient was less than [significance level], indicating statistical significance.

Model Assumption Evaluation

The assumptions of linear regression—linearity, normality, homoscedasticity, and independence—were assessed through diagnostic plots. Residual plots showed no obvious pattern, indicating linearity and homoscedasticity. Normal probability plots suggested residuals were approximately normally distributed. The independence assumption was deemed satisfied given the study design.

Prediction for a Specific Case

Using the regression equation, the BMI for an individual weighing 185 pounds was predicted, accompanied by 95% confidence and prediction intervals. The confidence interval reflects the range within which the mean BMI would fall for individuals with this weight, whereas the prediction interval estimates where a single new observation would likely lie. Both intervals demonstrated that BMI increases with weight, consistent with the model's findings.

Limitations on Model Use

Applying this adult-based model to a 10-year-old boy weighing 72 pounds would be inappropriate for two reasons: first, the model was developed using adult data, and BMI distributions differ significantly between children and adults; second, the relationship between weight and BMI may not be linear or the same across age groups, making predictions unreliable.

Conclusion

The analysis successfully developed a linear model linking weight to BMI in adults, providing quantitative insights and predictive capabilities. However, caution must be exercised when applying the model outside the adult population, especially to children, due to biological and statistical differences.

References

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