1. The problem is to determine the appropriate sample size for a multiple linear regression analysis based on power analysis and practical constraints. 2. The formula for power analysis in multiple regression involves parameters: power level ($1-\beta$), significance level ($\alpha$), effect size ($f^2$), and number of predictors ($k$). 3. Important rules: - Power level is the probability of correctly rejecting the null hypothesis (commonly set at 0.80 or higher). - Significance level $\alpha$ is the probability of Type I error (commonly 0.05). - Effect size $f^2$ quantifies the strength of the relationship; medium effect size is $f^2=0.15$. - Number of predictors affects degrees of freedom and sample size. 4. Given: $k=4$, $f^2=0.15$, $\alpha=0.05$, power levels 0.85 and 0.95. 5. Using power analysis software or tables, the minimum sample size for power 0.85 is 95 participants. 6. To increase power to 0.95, sample size must be at least 196 participants. 7. Due to project constraints (time, personnel), the sample size is capped at 200 participants, balancing power and practical feasibility. Final answer: The sample size is set between 95 (minimum for medium effect at power 0.85) and capped at 200 (to ensure power 0.95 and allow sufficient analysis time).