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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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A nutritionist records the amount of sugar (x, in grams) in ten different cereal brands and their average rating (y) given by a panel of tasters. The data are shown below.
Use your calculator to calculate the Pearson product–moment correlation coefficient, r.
Describe the correlation between sugar content and taste rating.
Find the equation of the regression line of y on x, in the form y=mx+c.
Estimate the expected taste rating when a cereal contains 15 grams of sugar.
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A health researcher measures each student’s average daily screen time x (in hours) and average nightly sleep y (in hours) for eight students:
Use your calculator to find the Pearson product–moment correlation coefficient, r, to 3 significant figures.
Find the equation of the regression line of y on x in the form y=mx+c.
Use your regression line to estimate the average sleep for a student with x=5.5 hours of screen time.
Interpret the value of r2 in the context of this study.
The researcher considers using the model to predict sleep for a student with x=10 hours of screen time.
Comment on the suitability of this prediction.
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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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On the seventh day, a new app begins a new advertising campaign. The developers record the number of new downloads at the end of each day.
Using the number of new downloads each day, find and interpret
the Pearson's coefficient
and the Spearman's coefficient.
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An astronaut measures the height above the moon's surface, h meters, of a rock t seconds after releasing it. The following table shows the recorded values of h and t2.
State the height from which the rock was released.
The relationship between h and t2 can be modeled by the equation h=at2+b.
Find the value of a and the value of b.
Hence estimate the time at which the rock reaches a height of 20 meters.
Explain why the regression equation should not be used to predict the height when t=9.
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