IDNLearn.com: Where your questions meet expert advice and community insights. Ask your questions and receive comprehensive, trustworthy responses from our dedicated team of experts.
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].
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your questions are important to us at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.