Regression In a study a regression model was fitted to a sample of data. This model indicates that there is a strong linear relationship between a car's age (measured in months) and a drop in its...

Regression

In a study a regression model was fitted to a sample of data. This model indicates that there is a strong linear relationship between a car's age (measured in months) and a drop in its price from new. Your friend sees these figures and thinks he can sell his car at a price obtained from this regression analysis. What would you say to him? Explain.

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mathsworkmusic | (Level 2) Educator

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The finding of a linear relationship between a car's age and it's depreciation in price suggests a guideline only. As George Box said "All models are wrong, but  some are useful". Models like this should always be used with discretion and caution. Pertinent questions are a) what is the quality of the data upon which the study is based? - particularly, is it a representative sample of the population of interest, ie an unbiased sample? b) how much data was collected? c) do the results agree with other studies? These sort of questions can help us decide on the credibility of the results and the usefulness of the model.

The regression line shows general tendency only and there will be natural variability about the line due to unmeasured factors and (perhaps) pure randomness. The buyer must be willing to pay the suggested price; competition between buyers might raise the price; the sales skills of the seller may have an effect; car make, model, specification, insurance class, colour and km on the clock (extent of usage) may affect how it's value depreciates over time - silver 5-door cars with large engines with few km on the clock will hold their value well for example.

The friend should realise that their car may be worth much less than when they bought it, buy roughly half or similar, but should not expect to get a very specific price for it. They could expect though not to get a price significantly higher than the model suggests because the buyer might have that sort of model in their mind if it is common knowledge. If the friend has time they should research further the price they might be able to get for their car considering as many factors as possible.

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