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General Mathematics Β· Unit 3 Β· Bivariate data analysis 2 Β· Fitting a linear model to numerical data

Interpret the 𝑦-intercept and slope (gradient) of the fitted line.

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Question 1

A biologist studying koala populations in a conservation reserve modelled the relationship between the number of years since 2010 (\(x\)) and the estimated koala population (\(y\)) using a least-squares regression line \(y = 12.4x + 287\). Interpret the slope of this fitted line.

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Question 2

A least-squares line was fitted to data on residential solar panel installations, with y representing the number of installations and x representing the number of months since January 2020 (e.g. x = 6 for July 2020). The fitted equation is y = 12.4x + 285. Interpret the y-intercept and slope of the fitted line.

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Distinguish between interpolation and extrapolation.
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Model a linear relationship by using technology to fit a least-squares line to the data, in the form of 𝑦 = π‘šπ‘₯ + 𝑐 where π‘š is slope (gradient) and 𝑐 is 𝑦-intercept.
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