Regression & Correlation (Grade 12) — Worksheet & Memo

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Grade 12 · Statistics

Regression & Correlation (Grade 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 16

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Using the scatter plot below, describe the type of relationship shown.
(2)
A strong positive linear relationship✓✓ (2)
2
The calculator gives A = 13,00 and B = 8,86. Write down the equation of the least squares regression line.
(2)
y = 13,00 + 8,86x✓✓ (2)
3
Use the regression line to predict the mark of a learner who studies for 7 hours.
(2)
13,00 + 8,86(7) ≈ 75,00%✓✓ (2)
4
Interpret the gradient of the regression line in this context.
(2)
Each extra hour of study is associated with about 8,86 more percentage points.✓✓ (2)
5
The correlation coefficient is r = 0,998. Interpret it.
(2)
A very strong positive linear correlation✓✓ (2)
6
What is the possible range of values for r?
(2)
−1 ≤ r ≤ 1✓✓ (2)
7
Would it be reasonable to use this line to predict the mark for 20 hours of study? Explain.
(2)
No — 20 hours is far outside the data range (1 to 6 hours) and the prediction would exceed 100%.✓✓ (2)
8
Does a strong correlation prove that studying causes higher marks?
(2)
No — correlation does not prove causation.✓✓ (2)

TOTAL: 16 marks