Interpreting the strength and direction of r

Name:

Date:

Class:

Quick Questions

Shade in the A or B circle for each question.

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)

2. Which r value shows the STRONGEST linear relationship?

A r = -0.92

B r = 0.60

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

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

5. Which r value is best described as a weak positive relationship?

A r = 0.25

B r = -0.25

Match the Pairs

Draw a line connecting each item on the left to its match on the right.

Left column		Right column
1r = -0.85		Ar = 0.30 -> r = 0.78
2r = 0.05		BNo real linear relationship: the points do not follow a straight line
3A positive r means that as x increases, y tends to increase as well		Cr = +0.62
4One outlier far from the other points can pull r up or down, so it can change the strength shown		DA strong negative linear relationship: as one variable rises, the other tends to fall
5r = -0.9, so there is a weak relationship		Er can never be outside the range -1 to 1, so 1.4 is impossible and means there was a calculation error.
6r = 1.4, so the relationship is very strong		FA negative sign shows direction, not weakness. The size 0.9 is close to 1, so this is a strong negative relationship.

Definitions

-1 <= r <= 1

Fill in the Blanks

Complete each line of code by filling in the missing parts.

=______(B2:B9,C2:C9)

IF r _ 0 THEN OUTPUT "Positive: y rises as x rises" ENDIF

IF ___(r) >= 0.7 THEN OUTPUT "Strong relationship" ENDIF

IF r >= __ AND r <= 1 THEN OUTPUT "Valid value of r" ENDIF

IF ABS(r) _ 0.3 THEN OUTPUT "Weak or no linear relationship" ENDIF

Spot the Error

Shade in the letter of the line that contains an 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)

Question 2

A r = -0.9

B if r > 0:

C print('negative')

D else:

E print('positive')

Question 3

A r = 0.92

B if abs(r) <= 0.7:

C print('strong')

Question 4

A r = 0.05

B if abs(r) < 0.2:

C print('almost no link')

D else

E print('some link')

Question 5

A r = -1.6

B if r < 0:

C print('falls as x rises')

Answer Key

Interpreting the strength and direction of r

Section A: Quick Questions

B — As screen time rises, sleep tends to fall (negative direction)

A — r = -0.92

A — There is almost no linear relationship

B — r always lies between -1 and 1

A — r = 0.25

Section B: 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.

Section C: Definitions

-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.

Section D: Fill in the Blanks

=CORREL(B2:B9,C2:C9)

IF r > 0 THEN
  OUTPUT "Positive: y rises as x rises"
ENDIF

IF ABS(r) >= 0.7 THEN
  OUTPUT "Strong relationship"
ENDIF

IF r >= -1 AND r <= 1 THEN
  OUTPUT "Valid value of r"
ENDIF

IF ABS(r) < 0.3 THEN
  OUTPUT "Weak or no linear relationship"
ENDIF

Section E: Spot the Error

A — The module is called statistics (with an s). It must be imported as 'import statistics as st' before st.correlation() can calculate r.

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.

B — Strength depends on how far r is from 0, so strong needs abs(r) >= 0.7. Using <= would label weak relationships as strong.

D — The else keyword must be followed by a colon. It should be 'else:'.

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.