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Currently, fixed static sensing is a primary way to monitor environmental data like air quality in cities. However, to obtain a dense spatial coverage, a large number of static monitors are required, thereby making it a costly option. Dense spatiotemporal coverage can be achieved using only a fraction of static sensors by deploying them on the moving vehicles, known as the drive by sensing paradigm. The redundancy present in the air quality data can be exploited by processing the sparsely sampled data to impute the remaining unobserved data points using the matrix completion techniques. However, the accuracy of imputation is dependent on the extent to which the moving sensors capture the inherent structure of the air quality matrix. Therefore, the challenge is to pick those set of paths (using vehicles) that perform representative sampling in space and time. Most works in the literature for vehicle subset selection focus on maximizing the spatiotemporal coverage by maximizing the number of samples for different locations and time stamps which is not an effective representative sampling strategy. We present regressive facility location-based drive by sensing, an efficient vehicle selection framework that incorporates the smoothness in neighboring locations and autoregressive time correlation while selecting the optimal set of vehicles for effective spatiotemporal sampling. We show that the proposed drive by sensing problem is submodular, thereby lending itself to a greedy algorithm but with performance guarantees. We evaluate our framework on selecting a subset from the fleet of public transport in Delhi, India. We illustrate that the proposed method samples the representative spatiotemporal data against the baseline methods, reducing the extrapolation error on the simulated air quality data. Our method, therefore, has the potential to provide cost effective dense air quality maps.