To determine the equation of the line of best fit for Natalie's data, follow these steps:
1. Collect the data points:
- Arm lengths (in cm): [tex]\[25, 35, 30, 0, 4, 3, 4, None, 20, None\][/tex]
- Distances (in cm): [tex]\[4011, 1294, None, 4, 4054, 2011, 24, None, 373, 338\][/tex]
2. Exclude missing data:
- Only include pairs where both arm length and distance are present.
- Valid pairs are:
[tex]\[
\begin{align*}
(25, 4011), \\
(35, 1294), \\
(0, 4), \\
(4, 4054), \\
(3, 2011), \\
(4, 24), \\
(20, 373).
\end{align*}
\][/tex]
3. Calculate the line of best fit:
- Using linear regression, determine the slope (m) and intercept (b) for the line. After performing these calculations, you get:
[tex]\[
\begin{align*}
\text{slope} (m) &= 20.168772563176898, \\
\text{intercept} (b) &= 1419.377385250129.
\end{align*}
\][/tex]
4. Form the equation of the line:
- The equation of the line of best fit is in the form [tex]\( y = mx + b \)[/tex].
- Plug in the calculated values for [tex]\(m\)[/tex] and [tex]\(b\)[/tex]:
[tex]\[
y = 20.168772563176898x + 1419.377385250129.
\][/tex]
5. Round the numbers to the nearest tenth:
- Slope ([tex]\(m\)[/tex]) rounded to the nearest tenth is [tex]\(20.2\)[/tex].
- Intercept ([tex]\(b\)[/tex]) rounded to the nearest tenth is [tex]\(1419.4\)[/tex].
6. Write the final equation:
[tex]\[
y = 20.2x + 1419.4.
\][/tex]
Therefore, the equation of the line of best fit for Natalie's data is [tex]\( y = 20.2x + 1419.4 \)[/tex].
