4.4 Correlation and linear regression Quiz

1. Which value of $r$ shows the strongest linear correlation?

• A. $0.8$
• B. $-0.3$
• C. $0.1$
• D. $-0.9$

2. A study finds a strong positive correlation between the number of firefighters at a fire and the damage caused. Which is the best comment?

• A. More firefighters cause more damage
• B. Larger fires need more firefighters and cause more damage, so correlation does not imply causation
• C. Damage causes firefighters to arrive
• D. The correlation must be weak

3. A regression line is $y=2.5x+4$. What does the value $2.5$ represent?

• A. The value of $y$ when $x=0$
• B. The correlation coefficient
• C. The average increase in $y$ for each one-unit increase in $x$
• D. The mean of $y$

4. The regression line $y=2.5x+4$ is based on data with $x$ from $1$ to $10$. Which prediction is least reliable?

• A. $x=3$
• B. $x=7.5$
• C. $x=9$
• D. $x=25$

5. Data have $\bar{x}=6$ and $\bar{y}=20$, with regression line $y=3x+b$. Find $b$.

• A. $2$
• B. $0$
• C. $6$
• D. $-2$