A group of students sat a test at the end of term. The number of lessons each student missed during the term and their score on the test are shown on the scatterplot.
- Describe the strength and direction of the linear association observed in this dataset. (2 marks)
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- Calculate the range of the test scores for the students who missed no lessons. (1 mark)
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- Draw a line of the best fit in the scatterplot above. (1 mark)
- Meg did not sit the test. She missed five lessons.
Use the line of the best fit drawn in part (c) to estimate Meg's score on this test. (1 mark)
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- John also did not sit the test and he missed 16 lessons.
Is it appropriate to use the line of the best fit to estimate his score on the test? Briefly explain your answer. (1 mark)
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a. \(\text{Strength : strong}\)
\(\text{Direction : negative} \)
b. \(\text{Range}\ = \text{high}-\text{low}\ = 100-80=20\)
c.
d.
e. \(\text{John’s missed days are too extreme and the LOBF is not}\)
\(\text{appropriate. The model would estimate a negative score for}\)
\(\text{John which is impossible.}\)
a. \(\text{Strength : strong}\)
\(\text{Direction : negative} \)
♦♦ Mean mark (b) 31%.
b. \(\text{Range}\ = \text{high}-\text{low}\ = 100-80=20\)
c.
d.
\(\therefore\ \text{Meg’s estimated score = 40}\)
e. \(\text{John’s missed days are too extreme and the LOBF is not}\)
\(\text{appropriate. The model would estimate a negative score for}\)
\(\text{John which is impossible.}\)
