1. **Stating the problem:** We need to analyze fabric output in textile manufacturing considering multiple influencing factors such as shift, machine type, fabric type, automation level, operator skill, loom speed, task time, break frequency, and worker experience. 2. **Theory and Methodology:** - Fabric output is the dependent variable measured in meters per day. - Independent variables include categorical factors (shift, machine type, fabric type, automation level, operator skill) and continuous variables (loom speed, task time, break frequency, worker experience). - Descriptive analysis summarizes data characteristics. - Advanced analysis explores relationships and impact of factors on fabric output. 3. **Descriptive Analysis:** - Use Excel to calculate mean, median, mode, standard deviation, and range for continuous variables. - Use frequency counts and percentages for categorical variables. - Visualize data with histograms, bar charts, and box plots. 4. **Method for Descriptive Analysis:** - Summarize central tendency and dispersion for continuous variables. - Summarize distribution of categorical variables. - Identify patterns or anomalies in data. 5. **Advanced Analysis:** - Use multiple linear regression to model fabric output as a function of all influencing factors. - Encode categorical variables using dummy variables. - Check assumptions: linearity, normality, homoscedasticity, multicollinearity. - Use ANOVA to test significance of categorical factors. - Use correlation analysis to assess relationships between continuous variables and output. 6. **Method for Advanced Analysis:** - Fit regression model: $$\text{Fabric Output} = \beta_0 + \beta_1 \times \text{Loom Speed} + \beta_2 \times \text{Task Time} + \beta_3 \times \text{Break Frequency} + \beta_4 \times \text{Worker Experience} + \sum \beta_i \times \text{Categorical Factors} + \epsilon$$ - Interpret coefficients to understand impact of each factor. - Validate model using residual analysis and goodness-of-fit metrics. 7. **Conclusion:** - This approach helps identify key factors affecting fabric output. - Enables optimization of production processes by focusing on significant variables. Final answer: Use Excel for descriptive statistics and visualization, then apply multiple linear regression and ANOVA for advanced analysis to understand and optimize fabric output based on the given factors.