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The severity of knee osteoarthritis is graded using the 5-point Kellgren-Lawrence (KL) scale where healthy knees are assigned grade 0, and the subsequent grades 1-4 represent increasing severity of the affliction. Although several methods have been proposed in recent years to develop models that can automatically predict the KL grade from a given radiograph, most models have been developed and evaluated on datasets not sourced from India. These models fail to perform well on the radiographs of Indian patients. In this paper, we propose a novel method using convolutional neural networks to automatically grade knee radiographs on the KL scale. Our method works in two connected stages: in the first stage, an object detection model segments individual knees from the rest of the image; in the second stage, a regression model automatically grades each knee separately on the KL scale. We train our model using the publicly available Osteoarthritis Initiative (OAI) dataset and demonstrate that fine-tuning the model before evaluating it on a dataset from a private hospital significantly improves the mean absolute error from 1.09 (95% CI: 1.03-1.15) to 0.28 (95% CI: 0.25-0.32). Additionally, we compare classification and regression models built for the same task and demonstrate that regression outperforms classification.