Scatter Plots & Association - Pre Algebra

1. What is the difference between a strong and a weak association on a scatter plot?

   In a strong association the points lie close to the pattern. In a weak one they are widely scattered around it.

2. How does a positive association appear on a scatter plot?

   The points tend to rise from left to right: larger $x$-values go with larger $y$-values.

3. What is the difference between a linear and a nonlinear association?

   In a linear association the points cluster around a straight line. In a nonlinear association they follow a curve.

4. How does a scatter plot with no association look?

   The points show no clear upward, downward or curved pattern.

5. What does a scatter plot display?

   Paired values of two numerical variables, each pair plotted as a point $(x, y)$.

6. On a scatter plot, the $y$-values rise quickly at first and then level off as $x$ increases. Is the association linear or nonlinear?

   Nonlinear. The points follow a curve rather than a straight line.

7. Describe the association shown by the points $(1, 2)$, $(2, 4)$, $(3, 6)$, $(4, 8)$.

   A perfect positive linear association. Every point lies on the line $y = 2x$.

8. On a scatter plot, which variable is usually placed on the $x$-axis?

   The explanatory (independent) variable, the one used to explain or predict the other.

9. What direction of association is expected between people's heights and their arm spans?

   Positive. Taller people tend to have longer arm spans.

10. How does a negative association appear on a scatter plot?

    The points tend to fall from left to right: larger $x$-values go with smaller $y$-values.

11. What is an outlier on a scatter plot?

    A point that lies far away from the overall pattern of the other points.

12. What direction of association is expected between the age of a car and its resale value?

    Negative. Older cars generally sell for less.

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