← VCE Data Analytics U4O1

Interpreting the strength and direction of r

The sign of r gives direction (+ rises, - falls); its size gives strength: near 1 or -1 is strong, near 0 means no linear link. Outliers can change r.

Part of: VCE Data Analytics - U4O1 - Development and Evaluation — Module 38

Understanding Interpreting the strength and direction of r in VCE Data Analytics U4O1

What it does: The plus sign means the direction is rising, and 0.62 is a moderate strength. Adding or removing one extreme point can change r a lot, so check for outliers before judging strength. A negative r means the two variables move in opposite directions: when one goes up, the other tends to go down. Strength depends on the size of r, ignoring the sign. 0.92 is closer to 1 than 0.60, so -0.92 is stronger. An r value near 0 means no linear relationship. The points do not follow a straight-line pattern. Pearson's r is always between -1 and +1 inclusive. A value outside this range means a calculation error.

Common mistakes: The module is called statistics (with an s). It must be imported as 'import statistics as st' before st.correlation() can calculate r. A negative r means a negative relationship. The test should be r < 0. With r > 0, the negative branch would print for positive values.

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Learning
Duo
A study finds r = -0.85 between hours of screen time and sleep. What does the sign tell you?
As screen time rises, sleep tends to fall (negative direction)As screen time rises, sleep tends to rise (positive direction)
Matches
r = -0.9, so there is a weak relationship
↓
A negative sign shows direction, not weakness. The size 0.9 is close to 1, so this is a strong negative relationship.
Applying
Meanings
Term
-1 <= r <= 1
Meaning
The sign of r gives direction (+ rises, - falls); its size gives strength: near 1 or -1 is strong, near 0 means no linear link. Outliers can change r.
Practice
=CORREL(B2:B9,C2:C9)
Testing
Gaps
=(B2:B9,C2:C9)
Check Answer
Spots
1import statistic as st
2x = [1, 2, 3, 4]

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Quick Questions

1. A study finds r = -0.85 between hours of screen time and sleep. What does the sign tell you?
A. As screen time rises, sleep tends to rise (positive direction)
B. As screen time rises, sleep tends to fall (negative direction) ✓
A negative r means the two variables move in opposite directions: when one goes up, the other tends to go down.
2. Which r value shows the STRONGEST linear relationship?
A. r = -0.92 ✓
B. r = 0.60
Strength depends on the size of r, ignoring the sign. 0.92 is closer to 1 than 0.60, so -0.92 is stronger.
3. A scatter plot of study hours and test marks gives r = 0.03. What is the best description?
A. There is almost no linear relationship ✓
B. There is a strong positive linear relationship
An r value near 0 means no linear relationship. The points do not follow a straight-line pattern.
4. Which statement about r is true?
A. r can be 2.5 if the relationship is very strong
B. r always lies between -1 and 1 ✓
Pearson's r is always between -1 and +1 inclusive. A value outside this range means a calculation error.
5. Which r value is best described as a weak positive relationship?
A. r = 0.25 ✓
B. r = -0.25
Both have the same weak strength, but only a positive sign means the variables rise together.

Match the Pairs

r = -0.85 → A strong negative linear relationship: as one variable rises, the other tends to fall
r = 0.05 → No real linear relationship: the points do not follow a straight line
A positive r means that as x increases, y tends to increase as well → r = +0.62
One outlier far from the other points can pull r up or down, so it can change the strength shown → r = 0.30 -> r = 0.78
r = -0.9, so there is a weak relationship → A negative sign shows direction, not weakness. The size 0.9 is close to 1, so this is a strong negative relationship.
r = 1.4, so the relationship is very strong → r can never be outside the range -1 to 1, so 1.4 is impossible and means there was a calculation error.

Key Term

-1 <= r <= 1
The sign of r gives direction (+ rises, - falls); its size gives strength: near 1 or -1 is strong, near 0 means no linear link. Outliers can change r.

Fill in the Blanks

1. =CORREL(B2:B9,C2:C9)
Hint: Type the spreadsheet function that calculates Pearson's r for two columns of data.
2. IF r > 0 THEN OUTPUT "Positive: y rises as x rises" ENDIF
Hint: Type the comparison operator that tests whether r is above zero, meaning an upward relationship.
3. IF ABS(r) >= 0.7 THEN OUTPUT "Strong relationship" ENDIF
Hint: Type the function that gives the size of r while ignoring its sign, so strength can be judged.
4. IF r >= -1 AND r <= 1 THEN OUTPUT "Valid value of r" ENDIF
Hint: Type the lowest value r can ever take.
5. IF ABS(r) < 0.3 THEN OUTPUT "Weak or no linear relationship" ENDIF
Hint: Type the comparison operator that tests whether the size of r is small, meaning a weak link.

Spot the Error

Question 1
A import statistic as st
B x = [1, 2, 3, 4]
C y = [2, 4, 6, 8]
D r = st.correlation(x, y)
E print(r)
Line A — The module is called statistics (with an s). It must be imported as 'import statistics as st' before st.correlation() can calculate r.
Question 2
A r = -0.9
B if r > 0:
C print('negative')
D else:
E print('positive')
Line B — A negative r means a negative relationship. The test should be r < 0. With r > 0, the negative branch would print for positive values.
Question 3
A r = 0.92
B if abs(r) <= 0.7:
C print('strong')
Line B — Strength depends on how far r is from 0, so strong needs abs(r) >= 0.7. Using <= would label weak relationships as strong.
Question 4
A r = 0.05
B if abs(r) < 0.2:
C print('almost no link')
D else
E print('some link')
Line D — The else keyword must be followed by a colon. It should be 'else:'.
Question 5
A r = -1.6
B if r < 0:
C print('falls as x rises')
Line A — r can only be between -1 and 1. A value of -1.6 is impossible, so it should be a value such as -0.6.

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