IB Maths AI HL AI 4.2 Correlation and regression questions

Exam-style questions in the shape of Paper 1 and Paper 2, with full markschemes. Read the markscheme, or type, photograph or draw your answer and get it marked.

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Question 1

Paper 1Hard6 marks

During a greenhouse trial, a horticulturist measures the height of a young plant on days 0 to 5. The measurements, rounded to the nearest centimetre, are shown in Figure 1.

01234505101520253035Elapsed time, x (days)Height, h (cm)(0, 8)(1, 10)(2, 14)(3, 18)(4, 25)(5, 31)
(a)

Use your GDC to fit a quadratic least-squares regression curve to the observations. Give its equation, R2R^2 and SSresSS_{\mathrm{res}}

[2]
(b)

Use your GDC to fit a linear least-squares regression curve to the observations. Give its R2R^2 SSresSS_{\mathrm{res}} and Pearson’s product moment correlation coefficient, rr Show numerically that R2=r2R^2=r^2 for this linear model.

[2]
(c)

A horticulturist claims that the quadratic model must be used to estimate the plant’s height on day 8 because it has the larger R2R^2 Assess this claim using the graph and your results.

[2]

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