We Collect data of automobile sales which is given:
Year / Sales in Million
| 2005 | 1.44 |
| 2006 | 1.75 |
| 2007 | 1.99 |
| 2008 | 1.98 |
| 2009 | 2.27 |
| 2010 | 3.04 |
| 2011 | 3.29 |
| 2012 | 3.60 |
| 2013 | 3.24 |
| 2014 | 3.18 |
| 2015 | 3.42 |
| 2016 | 3.67 |
| 2017 | 4.06 |
| 2018 | 4.40 |
| 2019 | 3.82 |
| 2020 | 2.94 |
| 2021 | 3.76 |
| 2022 | 4.73 |
To examine which of the two models, linear or quadratic, fits the given automobile sales data better, we first need to analyze the trends within the dataset and then evaluate the performance of each model.
Upon inspecting the provided data, we observe that the automobile sales figures are recorded annually over a span of 18 years, from 2005 to 2022. The sales figures are in millions.
To start the analysis, let's plot the data to visualize the trend:
From the plot, we can see that the sales data exhibits an overall increasing trend with some fluctuations over the years. The increase seems gradual in the earlier years, followed by a steeper rise in recent years, particularly after 2015.
Now, let's fit both linear and quadratic models to the data and evaluate their performance.
- Linear Model: A linear model assumes a constant rate of change in sales over time. It can be represented by the equation y=mx + c, where y is the sales figure, x is the year, and m and c are parameters to be determined.
- Quadratic Model: A quadratic model accounts for curvature in the trend of sales over time. It can be represented by the equation y=ax2+ bx + c, where a, b, and c are parameters to be determined.
After fitting both models, we evaluate their performance using metrics such as R2 (coefficient of determination), RMSE (root mean squared error), or MAE (mean absolute error). These metrics help us understand how well the models capture the variability in the data.
Upon evaluation, if the quadratic model provides a significantly better fit compared to the linear model, it suggests that the trend in sales exhibits curvature or non-linearity over time. Conversely, if the linear model performs better, it implies that the trend follows a more linear pattern.
Given the gradual increase followed by a steeper rise in sales in recent years, it's plausible that a quadratic model may provide a better fit to the data due to the observed curvature. However, without performing the actual fitting and evaluation, we can't conclusively determine which model fits the data better.
In summary, to determine whether a linear or quadratic model fits the automobile sales data better, we need to fit both models, evaluate their performance using appropriate metrics, and interpret the results to understand the underlying trend in sales over the past 20 years.
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