Linear Model Selection for Data Fitting

00:00 6 marks

A company has collected monthly sales data over the past year. The data suggests a linear trend in sales performance.

(a) Identify a suitable linear model to represent the data.

(b) Justify why this linear model is appropriate based on the nature of the data and the underlying factors influencing sales.

Part a

5 minutes 3 marks

Question

Propose a linear function of the form \(y = mx + c\) that could fit the given monthly sales data. Specify what each parameter (\(m\) and \(c\)) represents in this context.

Hint Hint

Hint

Think about how the slope (m) represents the rate of change in sales and how the intercept (c) represents the initial sales level.

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Answer Answer

Complete Answer

A possible model is \(y = mx + c\), where \(m\) represents the monthly change in sales and \(c\) represents the initial sales level at the start of the period.

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Part b

5 minutes 3 marks

Question

Discuss and justify why a linear model is appropriate for this data set, considering the nature of the business and other real-world factors.

Hint Hint

Hint

Consider factors such as steady growth trends, absence of seasonal variations, and external influences affecting sales.

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Complete Answer

A linear model is suitable because the sales data shows a constant monthly change, which reflects steady market conditions and consistent business operations. These factors support the assumption of a linear relationship between time and sales.

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