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Access custom-built, exam-style problems for bivariate statistics. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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The government of Mongolia surveys 6 herding families living in the valley of Yolyn to find out how many goats and sheep each family owns.
Find and interpret Pearson's product-moment correlation coefficient, r, for this data.
Find the equation of the regression line of s on g.
Use the regression line found in (b) to predict the number of goats (g) owned by a family in the valley with 205 sheep (s).
State two reasons why this prediction may not be accurate.
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Perplex conducts a study on student performance in IB math. The scores of 5 students are shown in the following table alongside the number of mock exams each student completed.
The relationship between S and N can be modelled by the regression line N=aS+b.
Find the value of a and the value of b.
Write down the correlation coefficient for this regression, and interpret its significance.
Using the regression equation, predict the number of mock exams completed by a student who scored a 3.
Suggest two reasons why this model cannot reliably predict the score of a student who completed 0 mock exams.
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The resting body temperature, in degrees °C, of 6 adults is measured and recorded alongside their age, in years, in the table below.
State the age of the outlier in this data set.
Suggest one reason the outlier identified in (a) should not be included in any further analysis.
The relationship between Y and C can be modelled by the equation C =aY+b.
Find the value of a and the value of b.
Find and interpret the value of Pearson's product-moment correlation coefficient, r, for these data.
Use the model C =aY+b to estimate the body temperature of a newborn, and explain why this is unlikely to be reliable.
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A teacher surveys his class to find out how long each student spent studying for a recent test. The time, in hours, each student spent studying is shown alongside their score in the following table.
Find and interpret Pearson's product-moment correlation coefficient, r, for this data.
Find the equation of the regression line of s on t.
Use the regression line found in (b) to predict the score of a student who spent 7 hours studying.
Explain why the regression equation should not be used to predict the score of a student who studied 25 hours for the test.
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The following table shows the data collected in a study.
Write down the values of xˉ and yˉ.
Using the grid below, draw a scatter diagram for the data.
Hence state any outlier(s) in the data.
Plot a line of best fit on your scatter plot, and hence estimate the regression equation of y on x.
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Using your regression equation, predict the value of y when x=3.
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