Lesson 5: Scatter Plots and Lines of Fit — Practice Questions

1. 1. Which statement correctly describes the relationship between association and correlation?

   • A. All associations are correlations.
   • B. All correlations are associations.
   • C. Association and correlation are unrelated concepts.
   • D. If there is no correlation, there can be no association.

2. 2. A scatter plot shows that as the speed of a car increases, its fuel efficiency increases up to a point, then decreases. How is this relationship best described?

   • A. Positive linear correlation
   • B. Negative linear correlation
   • C. Association but not a linear correlation
   • D. No association

3. 3. A person earns 15 dollars for each hour they work. Which term best describes the relationship between hours worked and money earned?

   • A. Positive correlation
   • B. Negative association only
   • C. A curved association
   • D. No association

4. 4. Correlation is a more specific term than association because it only describes a relationship that can be modeled with a straight line, which is also known as a ___ relationship.

5. 5. If a scatter plot shows that as one variable increases, the other variable also consistently increases, is this enough to guarantee a positive correlation?

   • A. Yes, because any positive trend is a positive correlation.
   • B. No, because the relationship could be a curve instead of a straight line.
   • C. Yes, because association and correlation mean the same thing.
   • D. No, because a positive trend could still have a negative correlation.

6. 6. A scatter plot shows plant height in cm versus weeks of growth. The line of best fit passes through the points $(3, 10)$ and $(7, 18)$. What is the slope of the line? ___

7. 7. A line of best fit for reading speed versus age passes through $(8, 110)$ and $(12, 150)$. Which equation correctly models this line?

   • A. y - 110 = 10(x - 8)
   • B. y - 8 = 10(x - 110)
   • C. y - 110 = 4(x - 8)
   • D. y - 150 = 40(x - 12)

8. 8. A line of best fit relates daily website visitors to an advertising budget in dollars. It passes through $(200, 5000)$ and $(500, 11000)$. What is the slope, representing visitors per dollar spent? ___

9. 9. A line of best fit for a scatter plot passes through the points $(4, 50)$ and $(10, 80)$. Which calculation correctly finds the slope of this line?

   • A. $m = \frac{80 - 50}{10 - 4}$
   • B. $m = \frac{10 - 4}{80 - 50}$
   • C. $m = \frac{80 + 50}{10 + 4}$
   • D. m = (80 - 50)(10 - 4)

10. 10. A line of best fit relates hours trained ($x$) to race time in minutes ($y$). The line passes through $(5, 30)$ and $(10, 25)$. If the equation is $y - 30 = m(x - 5)$, what is the value of $m$? ___