Problem Bank - Bivariate Statistics

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.

13 Problems Available

Select a Difficulty

IB: 4

IB: 5

IB: 6

IB: 4

0 / 7

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.

Study time (h)	0	1	2	4	5	8
Score (s)	45	52	62	65	74	88

Find and interpret Pearson's product-moment correlation coefficient, r, for this data.
[2]
Find the equation of the regression line of s on t.
[2]
Use the regression line found in (b) to predict the score of a student who spent 7 hours studying.
[2]
Explain why the regression equation should not be used to predict the score of a student who studied 25 hours for the test.
[1]

0 / 8

The resting body temperature, in degrees °C, of 6 adults is measured and recorded alongside their age, in years, in the table below.

Age (Y)	41	46	49	51	55	61
Temperature (C)	37.7	37.2	37.1	39.2	36.8	36.6

State the age of the outlier in this data set.
[1]
Suggest one reason the outlier identified in (a) should not be included in any further analysis.
[1]

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.
[2]
Find and interpret the value of Pearson's product-moment correlation coefficient, r, for these data.
[2]
Use the model C =aY+b to estimate the body temperature of a newborn, and explain why this is unlikely to be reliable.
[2]

0 / 9

The following table shows the data collected in a study.

x	1	2	4	5	6	8
y	18	29	54	32	69	93

Write down the values of xˉ and yˉ.
[2]
Using the grid below, draw a scatter diagram for the data.
[2]
Hence state any outlier(s) in the data.
[1]
Plot a line of best fit on your scatter plot, and hence estimate the regression equation of y on x.
[2]

Using your regression equation, predict the value of y when x=3.
[2]