← VCE Data Analytics U3O1

Interpreting the value of r

r always sits from -1 to 1. The sign shows direction (+ rises together, - one rises as other falls). Close to 0 is weak; close to 1 or -1 is strong.

Part of: VCE Data Analytics - U3O1 - Data Analytics — Module 89, ACARA Digital Technologies Years 9–10 — Analysing and Visualising Data — Module 45

Understanding Interpreting the value of r in VCE Data Analytics U3O1

What it does: The positive sign shows the variables rise together and 0.88 is close to 1, so it is a strong positive relationship. r is always between -1 and 1 inclusive, so a result such as 1.4 means a calculation mistake. A negative r means that as one variable increases, the other decreases. Strength depends on how close r is to 1 or -1, so ignore the sign. -0.80 is closer to -1 than 0.30 is to 1.

Common mistakes: r = 0.85 is positive (above 0) and close to 1, so the relationship is strong and positive, not negative. It should print "Strong positive". A negative r means one variable rises as the other falls. Both rising together describes a positive r. The line should print "One rises, other falls".

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Learning
Duo
A study finds r = 0.85 between hours studied and test score. What does this suggest?
A strong negative relationshipA strong positive relationship
Matches
r = -0.85, so the relationship is weak because it is negative
↓
The sign shows only direction, not strength. -0.85 is close to -1, so it is a strong negative relationship.
Applying
Meanings
Term
-1 <= r <= 1
Meaning
r always sits from -1 to 1. The sign shows direction (+ rises together, - one rises as other falls). Close to 0 is weak; close to 1 or -1 is strong.
Practice
=CORREL(B2:B8,D2:D8)
Testing
Gaps
-1 <= r <=
Check Answer
Spots
2if r > 0.7:
3 print("Strong negative")

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Quick Questions

1. A study finds r = 0.85 between hours studied and test score. What does this suggest?
A. A strong negative relationship
B. A strong positive relationship ✓
The sign is positive, so both variables rise together. 0.85 is close to 1, so the relationship is strong.
2. Which r value shows a negative relationship?
A. r = -0.62 ✓
B. r = 0.62
A minus sign means one variable rises as the other falls. A plus sign means they rise together.
3. Which r value shows the weakest relationship?
A. r = 0.05 ✓
B. r = -0.90
The closer r is to 0, the weaker the relationship. The minus sign only shows direction, not strength, so -0.90 is strong.
4. A student says r = 1.4 is a very strong relationship. Is this possible?
A. No, r must stay between -1 and 1 ✓
B. Yes, bigger numbers mean stronger
r always sits from -1 to 1. A value of 1.4 means the calculation has gone wrong.
5. Which statement about r = -0.95 is correct?
A. Weak: the minus sign makes it small
B. Strong: as one variable rises, the other falls ✓
-0.95 is close to -1, so it is strong. The negative sign shows direction only: one variable rises as the other falls.

Match the Pairs

r = -0.92 → A strong negative relationship: as one variable rises, the other tends to fall
r = 0.08 → A very weak relationship, so almost no linear pattern
A positive r means both variables tend to rise together, and a value near 1 makes it strong → r = 0.88
The value of r can never be outside the range from -1 to 1 → -1 <= r <= 1
r = -0.85, so the relationship is weak because it is negative → The sign shows only direction, not strength. -0.85 is close to -1, so it is a strong negative relationship.
r = 0.05, so there is a strong positive relationship → 0.05 is very close to 0, so the relationship is very weak, not strong. The positive sign only shows direction.

Key Term

-1 <= r <= 1
r always sits from -1 to 1. The sign shows direction (+ rises together, - one rises as other falls). Close to 0 is weak; close to 1 or -1 is strong.

Fill in the Blanks

1. -1 <= r <= 1
Hint: Type the largest value that r can ever reach.
2. =IF(CORREL(B2:B9,C2:C9)>0,"Up","Down")
Hint: Type the value that separates a positive r from a negative r.
3. =IF(ABS(D2)>0.7,"Strong","Weak")
Hint: Type the function that ignores the sign so only the size of r is tested.
4. IF r < 0 THEN DISPLAY "Negative" END IF
Hint: Type the number that r is compared with to find a negative relationship.
5. r = 0.05 is close to 0, so it is weak
Hint: Type the word describing the strength of a relationship when r is near zero.

Spot the Error

Question 1
A r = 0.85
B if r > 0.7:
C print("Strong negative")
Line C — r = 0.85 is positive (above 0) and close to 1, so the relationship is strong and positive, not negative. It should print "Strong positive".
Question 2
A r = -0.9
B if r < 0:
C print("Both rise together")
Line C — A negative r means one variable rises as the other falls. Both rising together describes a positive r. The line should print "One rises, other falls".
Question 3
A r = 1.4
B if r >= -1 and r <= 1:
C print("Valid r value")
Line A — r can only be between -1 and 1, so 1.4 is impossible. The value must be within that range, for example r = 0.4.
Question 4
A r = 0.05
B if abs(r) > 0.3:
C print("Weak relationship")
Line B — A weak relationship has r close to 0, so abs(r) should be small. The test should be abs(r) < 0.3, not greater than 0.3.
Question 5
A r = -0.8
B strength = abs(r)
C if strength > 0.7:
D print("Weak negative")
Line D — r = -0.8 is close to -1, so the relationship is strong. Its size (0.8) is large, so it should print "Strong negative".

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