## Math Problem Statement

Use concepts on chi square test of association and homogeniety, correlation analysis, and simple linear regression analysis.

## Solution

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## Math Problem Analysis

### Mathematical Concepts

Chi-square test of association

Hypothesis testing

Correlation analysis

Simple linear regression

### Formulas

Chi-square statistic: \(\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}\)

Expected value for Chi-square: \(E = \frac{(\text{Row total} \times \text{Column total})}{\text{Grand total}}\)

Simple linear regression: \(Y = \beta_0 + \beta_1 X + \epsilon\)

### Theorems

Chi-square test of independence

Linear regression model assumptions

### Suitable Grade Level

Undergraduate

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