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Sagot :
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].
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].
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