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IB Maths AI SL 4.4 Correlation and Regression Questions

Practise interpreting scatter plots and correlation, using y-on-x regression for prediction, and judging residuals, extrapolation and causation limits.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation SL
Level
SL

Exam points

  • Interpret scatter diagrams and Pearson correlation coefficient for direction and strength, distinguishing correlation from causation.
  • Use a y-on-x regression line to estimate or predict a response and interpret gradient/intercept.
  • Assess residuals, extrapolation and the reliability or limitations of a regression conclusion.

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Study SL 4.4—Correlation and regression conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

IB Maths AI SL 4.4 Correlation and Regression Questions question 1

[Maximum number: 5]

The mean annual temperatures for Earth, recorded at fifty-year intervals, are shown in the table.

Table for Question IB Maths AI SL 4.4 Correlation and Regression Questions question 1 — IB Maths AI SL

Tami creates a linear model for this data by finding the equation of the straight line passing through the points with coordinates (1708,8.73) and (1958,9.45).

Question (a)

(a)

Thandizo uses linear regression to obtain a model for the data.

[ 3 ]

Question (i)

(i)

Find the equation of the regression line y on x.

[ 2 ]

Question (ii)

(ii)

Find the value of r, the Pearson's product-moment correlation coefficient.

[ 1 ]

Question (b)

(b)

Use Thandizo's model to estimate the mean annual temperature in the year 2000.

[ 2 ]
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