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Question 1
A company records monthly advertising spend ( $x$ , in thousands of dollars) and monthly sales ( $y$ , in thousands of dollars) for 10 months. The GDC output gives $r = 0.87$ . Which statement best describes this correlation?
No clue? Show me the answer
Correct answerCorrect!Incorrect
AStrong positive linear correlation
Step-by-step walkthrough
Choose a solution method
Method #1Worked solution
Step 1: Locate the value
We are given $r = 0.87$ , which is positive and close to 1.
Step 2: Apply the guideline table
Since $0.75 \leq r < 1$ , this falls in the 'strong positive correlation' band.
Step 3: State conclusion
A strong positive linear correlation exists between advertising spend and sales.
Step 4: Choose option
This matches option B.
Method #2Why the others are wrong
Step 1: Option A
Weak positive would require $r$ between 0 and 0.5, not 0.87.
Step 2: Option C
Negative correlation requires a negative $r$ value, but $r = 0.87 > 0$ .
Step 3: Option D
No correlation would mean $r \approx 0$ , not 0.87.
Step 4: Confirm
Only strong positive correctly matches $r = 0.87$ .
Question 2
A scatter diagram of a car's age ( $x$ , years) against its resale value ( $y$ , thousands of dollars) shows points sloping downward, tightly clustered around a straight line. Which correlation coefficient value is most consistent with this diagram?
No clue? Show me the answer
Correct answerCorrect!Incorrect
B $r = - 0.95$
Step-by-step walkthrough
Choose a solution method
Method #1Worked solution
Step 1: Direction
Points slope downward, so as $x$ increases, $y$ decreases — a negative correlation.
Step 2: Strength
Points are tightly clustered around a line, indicating a strong correlation, so $∣ r ∣$ should be close to 1.
Step 3: Combine
Negative and strong means $r$ close to $- 1$ .
Step 4: Choose option
$r = - 0.95$ matches both direction and strength.
Method #2Why the others are wrong
Step 1: Option A
$r = 0.95$ is positive, implying an upward slope, which contradicts the description.
Step 2: Option C
$r = - 0.10$ is far too close to zero for a tightly clustered pattern.
Step 3: Option D
$r = 0.10$ has both wrong sign and wrong magnitude.
Step 4: Confirm
Only $r = - 0.95$ fits a strong, negative, linear pattern.

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14 more questions in this topic

Free preview 2/16

Question 1
A company records monthly advertising spend ( $x$ , in thousands of dollars) and monthly sales ( $y$ , in thousands of dollars) for 10 months. The GDC output gives $r = 0.87$ . Which statement best describes this correlation?
No clue? Show me the answer
Correct answerCorrect!Incorrect
AStrong positive linear correlation
Step-by-step walkthrough
Choose a solution method
Method #1Worked solution
Step 1: Locate the value
We are given $r = 0.87$ , which is positive and close to 1.
Step 2: Apply the guideline table
Since $0.75 \leq r < 1$ , this falls in the 'strong positive correlation' band.
Step 3: State conclusion
A strong positive linear correlation exists between advertising spend and sales.
Step 4: Choose option
This matches option B.
Method #2Why the others are wrong
Step 1: Option A
Weak positive would require $r$ between 0 and 0.5, not 0.87.
Step 2: Option C
Negative correlation requires a negative $r$ value, but $r = 0.87 > 0$ .
Step 3: Option D
No correlation would mean $r \approx 0$ , not 0.87.
Step 4: Confirm
Only strong positive correctly matches $r = 0.87$ .
Question 2
A scatter diagram of a car's age ( $x$ , years) against its resale value ( $y$ , thousands of dollars) shows points sloping downward, tightly clustered around a straight line. Which correlation coefficient value is most consistent with this diagram?
No clue? Show me the answer
Correct answerCorrect!Incorrect
B $r = - 0.95$
Step-by-step walkthrough
Choose a solution method
Method #1Worked solution
Step 1: Direction
Points slope downward, so as $x$ increases, $y$ decreases — a negative correlation.
Step 2: Strength
Points are tightly clustered around a line, indicating a strong correlation, so $∣ r ∣$ should be close to 1.
Step 3: Combine
Negative and strong means $r$ close to $- 1$ .
Step 4: Choose option
$r = - 0.95$ matches both direction and strength.
Method #2Why the others are wrong
Step 1: Option A
$r = 0.95$ is positive, implying an upward slope, which contradicts the description.
Step 2: Option C
$r = - 0.10$ is far too close to zero for a tightly clustered pattern.
Step 3: Option D
$r = 0.10$ has both wrong sign and wrong magnitude.
Step 4: Confirm
Only $r = - 0.95$ fits a strong, negative, linear pattern.

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SL 4.4—Correlation of Data

Step-by-step walkthrough

Step 1: Locate the value

Step 2: Apply the guideline table

Step 3: State conclusion

Step 4: Choose option

Step 1: Option A

Step 2: Option C

Step 3: Option D

Step 4: Confirm

Step-by-step walkthrough

Step 1: Direction

Step 2: Strength

Step 3: Combine

Step 4: Choose option

Step 1: Option A

Step 2: Option C

Step 3: Option D

Step 4: Confirm

14 more questions in this topic

SL 4.4—Correlation of Data

Step-by-step walkthrough

Step 1: Locate the value

Step 2: Apply the guideline table

Step 3: State conclusion

Step 4: Choose option

Step 1: Option A

Step 2: Option C

Step 3: Option D

Step 4: Confirm

Step-by-step walkthrough

Step 1: Direction

Step 2: Strength

Step 3: Combine

Step 4: Choose option

Step 1: Option A

Step 2: Option C

Step 3: Option D

Step 4: Confirm

14 more questions in this topic