Multiple Choice

1. What type of association exists between 'fitness level' and 'amount of daily exercise'?

   Association exists; Positive

   No meaningful association

   Association exists; Negative

   Association exists; Non-linear

2. What type of association exists between 'foot length' and 'height'?

   Association exists; Negative

   No meaningful association

   Association exists; Positive

   Association exists; Non-linear

3. What type of association exists between 'comfort level' and 'temperature above $30^\circ\text{C}$'?

   Association exists; Positive

   Association exists; Non-linear

   No meaningful association

   Association exists; Negative

4. What type of association is expected between 'foot length' and 'intelligence'?

   Association exists; Positive

   Association exists; Negative

   No meaningful association expected

   Association exists; Linear

5. What type of association exists between 'time taken to get to school' and 'distance travelled'?

   Association exists; Non-linear

   No meaningful association

   Association exists; Negative

   Association exists; Positive

6. What type of association exists between 'number of pages in a book' and its 'price'?

   Association exists; Positive

   Association exists; Non-linear

   No meaningful association

   Association exists; Negative

7. How is the association in scatterplot (a), 'Mark (%)' vs 'Time (hours)', classified?

   
   Strength: weak; Form: linear; Direction: positive; Outliers: none clearly evident.

   Strength: moderately strong; Form: non-linear; Direction: positive; Outliers: none clearly evident.

   Strength: moderately strong; Form: linear; Direction: positive; Outliers: none clearly evident.

   Strength: moderately strong; Form: linear; Direction: negative; Outliers: none clearly evident.

8. How is the association in scatterplot (b), 'Price (\$000)' vs 'Age (years)', classified?

   
   Strength: strong; Form: non-linear; Direction: negative; Outliers: none apparent.

   Strength: strong; Form: approximately linear; Direction: negative; Outliers: none apparent.

   Strength: strong; Form: approximately linear; Direction: positive; Outliers: none apparent.

   Strength: weak; Form: approximately linear; Direction: negative; Outliers: none apparent.

9. How is the association in scatterplot (c), 'Daughter's height (cm)' vs 'Mother's height (cm)', classified?

   
   Strength: moderate; Form: linear; Direction: negative; Outliers: none obvious.

   Strength: moderate; Form: non-linear; Direction: positive; Outliers: none obvious.

   Strength: moderate; Form: linear; Direction: positive; Outliers: none obvious.

   Strength: strong; Form: linear; Direction: positive; Outliers: none obvious.

10. How is the association in scatterplot (d), 'Performance level' vs 'Time spent practising', classified?

    
    Strength: strong; Form: non-linear (increasing with diminishing returns); Direction: positive; Outliers: none.

    Strength: weak; Form: non-linear (increasing with diminishing returns); Direction: positive; Outliers: none.

    Strength: strong; Form: linear; Direction: positive; Outliers: none.

    Strength: strong; Form: non-linear (decreasing); Direction: negative; Outliers: none.

11. How is the association in scatterplot (e), 'Score on test' vs 'Temperature ($^\circ\text{C}$)', classified?

    
    Strength: weak to moderate; Form: non-linear (curved, overall decrease at higher temperatures); Direction: overall negative; Outliers: none clear.

    Strength: weak to moderate; Form: non-linear (curved, overall decrease at higher temperatures); Direction: overall positive; Outliers: none clear.

    Strength: strong; Form: non-linear (curved, overall decrease at higher temperatures); Direction: overall negative; Outliers: none clear.

    Strength: weak to moderate; Form: linear; Direction: overall negative; Outliers: none clear.

12. How is the association in scatterplot (f), 'Wife's age (years)' vs 'Husband's age (years)', classified?

    
    Strength: moderate to strong; Form: non-linear; Direction: positive; Outliers: one evident point with wife substantially older than husband.

    Strength: weak; Form: linear (near $y=x$); Direction: positive; Outliers: one evident point with wife substantially older than husband.

    Strength: moderate to strong; Form: linear (near $y=x$); Direction: negative; Outliers: none.

    Strength: moderate to strong; Form: linear (near $y=x$); Direction: positive; Outliers: one evident point with wife substantially older than husband.

13. Compute $r$ for $x=\{1,2,3\}$ and $y=\{4,8,12\}$.

    $r=-1$

    $r=1$

    $r=0$

    $r=0.5$

14. Compute $r$ for $x=\{-2,0,2\}$ and $y=\{2,0,-2\}$.

    $r=0$

    $r=1$

    $r=0.5$

    $r=-1$

15. Compute $r$ for $x=\{-1,0,1\}$ and $y=\{1,0,1\}$.

    $r=1$

    $r=0.5$

    $r=0$

    $r=-1$

16. Compute $r$ for $x=\{1,-1,0\}$ and $y=\{1,0,-1\}$.

    $r=0$

    $r=1$

    $r=-1$

    $r=\tfrac{1}{2}$

17. Given $n=3$, $\sum x=0$, $\sum y=0$, $\sum x^2=2$, $\sum y^2=2$, and $\sum xy=1$, find $r$.

    $r=0$

    $r=-1$

    $r=1$

    $r=\tfrac{1}{2}$

18. If $X' = 10X+7$ and $Y' = 5Y-3$, how does the correlation change?

    Unchanged; $r' = r$

    $r' = 5r$

    $r' = 10r$

    $r' = -r$