This study is conducted to evaluate the effectiveness of Covid-19 vaccines in different age groups in Saskatchewan, Canada. Data was collected between September 2021 and December 2021, and a statistical method called multinomial logistic regression was used to analyze the relationships between multiple categorical variables. In this study, the categorical variables were the age groups and the vaccination status (fully vaccinated cases, partially vaccinated cases, and unvaccinated cases) of the individuals with the interaction effect of rate of cases. The mathematical proof for the multinomial logistic regression model with interaction effect was derived in this study. The study demonstrated the effectiveness of Covid-19 vaccines among vaccinated age groups and provided theory and practical application of the multinomial logistic regression model. Results show that there is a statistically significant impact of age group and vaccination status on the effectiveness of Covid-19 cases in Saskatchewan. Specifically, there is a difference in vaccine effectiveness based on age groups and vaccination status. The findings of this study provide crucial insights for policymakers and public health officials to optimize vaccination rollout strategies and control the spread of Covid-19. Overall, this study represents an important step in the ongoing efforts to understand the effectiveness of Covid-19 vaccines and to develop policies and interventions that can help mitigate the pandemic impact.