Correlation

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Correlation — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionLines of best fitAssessment Practice

6 marks~9 minCriterion C

The scatter diagram below shows test scores (out of 100) and revision times (in hours) for 10 students. A line of best fit has been drawn with equation

y = 8x + 28

where

x

is revision time in hours and

y

is the predicted test score.

The table below shows actual and predicted scores for three students.

$x$ (hours)	2	5	8
Predicted $y$	44	68	92
Actual $y$	50	65	80

Write down the

y

-intercept of the line of best fit and interpret its meaning in this context. [2]

Calculate the percentage error for the student who revised for 8 hours, using

\text{percentage error} = \frac{|\text{predicted} - \text{actual}|}{\text{actual}} \times 100\%.

Give your answer correct to 1 decimal place. [2]

A student claims the model is equally reliable for predicting scores at 2 hours and at 8 hours of revision. Using the percentage errors for both

x = 2

and

x = 8

, assess whether this claim is correct. [2]

Solutions

2QuestionLines of best fitAssessment Practice

7 marks~11 minCriterion B

The diagram shows Figures 1, 2 and 3 of a pattern made from unit squares arranged in rectangles.

Figure ( $n$ )	1	2	3
Squares ( $S$ )	3	8	15

Write down the number of unit squares in Figure 4. [1]

Find a rule for the number of unit squares

S

in Figure

n

. Show that your rule can be written in the form

S = n(n + 2).

[3]

A student claims that

S

is always an odd number when

n

is odd. Justify this claim using your rule, then determine whether Figure 13 is the only figure for which

S = 195

, giving a reason for your answer. [3]

Solutions

3QuestionLines of best fitAssessment Practice

7 marks~11 minCriterion D

A survey records the number of hours studied per week (

x

) and the test score (

y

, out of 100) for 10 students. A line of best fit is drawn with equation

y = 8x + 30.

The table below shows predicted and actual scores for three students.

$x$ (hours)	2	5	8
Predicted $y$	46	70	94
Actual $y$	50	65	88

Calculate the percentage error for the student who studied for 5 hours, using

\text{percentage error} = \frac{|\text{predicted} - \text{actual}|}{\text{actual}} \times 100\%.

Give your answer to 2 significant figures. [2]

A student claims she studied for 7 hours and scored 90. Deduce whether her score is above or below the score predicted by the model, and find the exact difference. [2]

Another student scored 74 on the test. Using the model, find the number of hours this student is predicted to have studied. Hence advise whether a teacher should use this model to predict the score of a student who studies for 12 hours, justifying your answer with reference to the data given. [3]

Solutions

4QuestionLines of best fitAssessment Practice

12 marks~18 minCriterion A

The table below shows the number of hours studied (

x

) and the test score (

y

) for 8 students.

x

(hours): 2, 3, 5, 6, 8, 9, 11, 14

y

(score): 55, 60, 72, 78, 85, 82, 95, 68

State the coordinates of the point that appears to be an outlier, and give one reason why it is unusual. [2]

Using all 8 data points, calculate the equation of the line of best fit in the form

y = mx + c

, giving

m

and

c

each to 3 significant figures. Use the formulas

m = \frac{n\sum xy - \sum x\, \sum y}{n\sum x^2 - \left(\sum x\right)^2}, \qquad c = \frac{\sum y - m\sum x}{n}.

Hence predict the test score for a student who studies for 10 hours, giving your answer to the nearest integer. [5]

The outlier is removed. A student claims that removing this single point will increase the gradient of the line of best fit by more than 100%. Recalculate

m

and

c

for the remaining 7 data points (each to 3 significant figures) and justify whether the student's claim is correct. [5]

Solutions

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