Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Get quick and reliable solutions to your questions from a community of experienced experts on our platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To determine which equation best models the given data set, let's examine each option step-by-step and compare their residuals.
1. Equation A: [tex]\( y = 2x + 17 \)[/tex]
- Here, for each [tex]\( x \)[/tex] value given in the table, compute [tex]\( y \)[/tex] using the equation [tex]\( y = 2x + 17 \)[/tex].
- Then, compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values from the table and calculate the sum of the squared differences (residuals) between the actual and computed [tex]\( y \)[/tex] values.
2. Equation B: [tex]\( y = 11\sqrt{x - 0.3} + 4.3 \)[/tex]
- For each [tex]\( x \)[/tex] value given in the table, compute [tex]\( y \)[/tex] using the equation [tex]\( y = 11\sqrt{x - 0.3} + 4.3 \)[/tex].
- Compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values from the table and calculate the sum of the squared differences (residuals).
3. Equation C: [tex]\( y = 2x - 17 \)[/tex]
- For each [tex]\( x \)[/tex] value, compute [tex]\( y \)[/tex] using [tex]\( y = 2x - 17 \)[/tex].
- Compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values and calculate the sum of the squared residuals.
4. Equation D: [tex]\( y = 11\sqrt{x + 0.3} - 4.3 \)[/tex]
- For each [tex]\( x \)[/tex] value, compute [tex]\( y \)[/tex] using [tex]\( y = 11\sqrt{x + 0.3} - 4.3 \)[/tex].
- Compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values and calculate the sum of the squared residuals.
By comparing the sum of the squared residuals for each model, the one with the smallest residuals will be the best fit model. This process involves calculations for each equation using the provided values and comparing the accuracy.
After performing this comparison, we find that the equation [tex]\( \boxed{y = 11\sqrt{x - 0.3} + 4.3} \)[/tex] (option B) results in the smallest sum of squared residuals and, hence, best models the provided data set.
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
1. Equation A: [tex]\( y = 2x + 17 \)[/tex]
- Here, for each [tex]\( x \)[/tex] value given in the table, compute [tex]\( y \)[/tex] using the equation [tex]\( y = 2x + 17 \)[/tex].
- Then, compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values from the table and calculate the sum of the squared differences (residuals) between the actual and computed [tex]\( y \)[/tex] values.
2. Equation B: [tex]\( y = 11\sqrt{x - 0.3} + 4.3 \)[/tex]
- For each [tex]\( x \)[/tex] value given in the table, compute [tex]\( y \)[/tex] using the equation [tex]\( y = 11\sqrt{x - 0.3} + 4.3 \)[/tex].
- Compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values from the table and calculate the sum of the squared differences (residuals).
3. Equation C: [tex]\( y = 2x - 17 \)[/tex]
- For each [tex]\( x \)[/tex] value, compute [tex]\( y \)[/tex] using [tex]\( y = 2x - 17 \)[/tex].
- Compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values and calculate the sum of the squared residuals.
4. Equation D: [tex]\( y = 11\sqrt{x + 0.3} - 4.3 \)[/tex]
- For each [tex]\( x \)[/tex] value, compute [tex]\( y \)[/tex] using [tex]\( y = 11\sqrt{x + 0.3} - 4.3 \)[/tex].
- Compare the computed [tex]\( y \)[/tex] with the actual [tex]\( y \)[/tex] values and calculate the sum of the squared residuals.
By comparing the sum of the squared residuals for each model, the one with the smallest residuals will be the best fit model. This process involves calculations for each equation using the provided values and comparing the accuracy.
After performing this comparison, we find that the equation [tex]\( \boxed{y = 11\sqrt{x - 0.3} + 4.3} \)[/tex] (option B) results in the smallest sum of squared residuals and, hence, best models the provided data set.
Therefore, the correct answer is:
[tex]\[ \boxed{B} \][/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.
