The increase in air pollution levels in recent decades around the world has caused a negative impact on human health. A recent investigation by the World Health Organization indicates that nine out of ten people on the planet breathe air containing high levels of pollutants and seven million people die each year from this cause. This problem is present in several cities in South America due to dangerous levels of particulate matter present in the air, particularly in the winter period, making it a public health problem. Santiago in Chile and Lima in Peru are among the ten cities with the highest levels of air pollution in South America. The location, climate, and anthropogenic conditions of these cities generate critical episodes of air pollution, especially in the coldest months. In this context, we developed a semiparametric model to predict particulate matter levels as a function of meteorological variables. For this, we discuss estimation and diagnostic procedures using a Student's t-based partially varying coefficient model. Parameter estimation is performed through the penalized maximum likelihood method using smoothing splines. To obtain the parameter estimates, we present a weighted back-fitting algorithm implemented in R-project and Matlab software. In addition, we developed local influence techniques that allowed us to evaluate the potential influence of certain observations in the model using four different perturbation schemes. Finally, we applied the developed model to real data on air pollution and meteorological variables in Santiago and Lima.