**Data Collection:**

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- Obtain historical data on automobile sales from a reliable source, such as the company’s official reports, industry databases, or government publications.

**Data Preprocessing:**

- Clean and organize the data, ensuring it includes sales figures and corresponding time periods (years).

**Visualization:**

- Plot the sales data against time to visualize the trend. This can help you identify whether a linear or quadratic relationship seems more appropriate.

**Model Fitting:**

- Fit both the linear and quadratic models to the data.
- Use statistical techniques, such as the least squares method, to estimate the coefficients for each model.

**Model Comparison:**

- Conduct statistical tests to compare the goodness-of-fit for the linear and quadratic models. The F-test or likelihood ratio test are common choices.

**Evaluate Residuals:**

- Examine the residuals (the differences between observed and predicted values) for both models. A good fit should result in residuals that are randomly distributed around zero.

**Validation:**

- If available, use a separate set of data or a time period not used in model fitting to validate the performance of the chosen model.

Remember that the choice between a linear and quadratic model should be based on both statistical tests and the practical interpretability of the results. Overfitting should also be considered; a more complex model might fit the existing data well but may not generalize to new data.

For an accurate analysis, it’s recommended to use statistical software like R, Python (with libraries like NumPy, SciPy, and statsmodels), or specialized tools for regression analysis.