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The coronavirus outbreak is the most notable world crisis since the Second World War. The pandemic that originated from Wuhan, China in late 2019 has affected all the nations of the world and triggered a global economic crisis whose impact will be felt for years to come. This necessitates the need to monitor and predict COVID-19 prevalence for adequate control. The linear regression models are prominent tools in predicting the impact of certain factors on COVID-19 outbreak and taking the necessary measures to respond to this crisis. The data was extracted from the NCDC website and spanned from March 31, 2020 to May 29, 2020. In this study, we adopted the ordinary least squares estimator to measure the impact of travelling history and contacts on the spread of COVID-19 in Nigeria and made a prediction. The model was conducted before and after travel restriction was enforced by the Federal government of Nigeria. The fitted model fitted well to the dataset and was free of any violation based on the diagnostic checks conducted. The results show that the government made a right decision in enforcing travelling restriction because we observed that travelling history and contacts made increases the chances of people being infected with COVID-19 by 85% and 88% respectively. This prediction of COVID-19 shows that the government should ensure that most travelling agency should have better precautions and preparations in place before re-opening.