Question

a. write the equation for the best - fit line for the data. round to the nearest hundredth, if necessary.
y = \boxed{0.26}x + \boxed{21.21}
part b
b. find and interpret the correlation coefficient.
r=\boxed{0.359}
the equation \boxed{select choice} the data well. its value means that as the years since the 2011 - 2012 school year increase,
the percentage of students in public school who met all six of californias physical fitness standards each year
\boxed{select choice}.
c. what constraints are there in the situation? explain.
because the data on the students who meet all six standards is reported as a percentage, it cannot exceed
\boxed{select choice}.

Explanation:

Part B - b.

1. Correlation Coefficient Interpretation: The correlation coefficient \( r = 0.359 \) is positive, indicating a positive linear relationship. Since \( |r| \) is between 0 and 0.5, the linear relationship is weak. So the equation does not fit the data well (because a weak correlation means the linear model isn't a strong fit), and as \( x \) (years since 2011 - 2012) increases, \( y \) (percentage of students meeting standards) increases slightly (due to positive \( r \)).
2. First Dropdown ("The equation... the data well"): Since \( r = 0.359 \) is a weak positive correlation, the linear equation does not fit the data well. So the first "Select Choice" should be "does not fit".
3. Second Dropdown ("as the years... each year"): Since \( r \) is positive, as \( x \) (years) increases, \( y \) (percentage) increases. But because the correlation is weak, it's a slight increase, so the second "Select Choice" should be "increases slightly".

A percentage cannot exceed 100% (since 100% represents the entire population of students). So the "Select Choice" for the percentage constraint should be "100%".

Answer:

\( r = 0.359 \)
The equation \(\boldsymbol{\text{does not fit}}\) the data well. Its value means that as the years since the 2011–2012 school year increase, the percentage of students in public school who met all six of California’s physical fitness standards each year \(\boldsymbol{\text{increases slightly}}\).

Part B - c.