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Answer :
To predict the [tex]\( y \)[/tex]-value for an [tex]\( x \)[/tex]-value of 200 using the quadratic regression equation [tex]\( y = 0.008x^2 + 0.518x + 131.886 \)[/tex], you need to substitute the [tex]\( x \)[/tex]-value into the equation. Here's how you can do it step-by-step:
1. Identify the quadratic regression equation:
The equation provided is [tex]\( y = 0.008x^2 + 0.518x + 131.886 \)[/tex].
2. Substitute [tex]\( x = 200 \)[/tex] into the equation:
Replace [tex]\( x \)[/tex] with 200 in the equation. So it becomes:
[tex]\[
y = 0.008(200)^2 + 0.518(200) + 131.886
\][/tex]
3. Calculate each term separately:
- First, calculate [tex]\( 0.008 \times (200)^2 \)[/tex]:
[tex]\( (200)^2 = 40000 \)[/tex]
[tex]\( 0.008 \times 40000 = 320 \)[/tex]
- Then, calculate [tex]\( 0.518 \times 200 \)[/tex]:
[tex]\( 0.518 \times 200 = 103.6 \)[/tex]
4. Add these results to the constant term (131.886):
[tex]\[
y = 320 + 103.6 + 131.886
\][/tex]
5. Calculate the final result:
Add the numbers together:
[tex]\( y = 555.486 \)[/tex]
Based on these calculations, the predicted [tex]\( y \)[/tex]-value when [tex]\( x = 200 \)[/tex] is approximately 555.5, which matches option d.
Therefore, the answer is:
d. [tex]\( y = 555.5 \)[/tex]
1. Identify the quadratic regression equation:
The equation provided is [tex]\( y = 0.008x^2 + 0.518x + 131.886 \)[/tex].
2. Substitute [tex]\( x = 200 \)[/tex] into the equation:
Replace [tex]\( x \)[/tex] with 200 in the equation. So it becomes:
[tex]\[
y = 0.008(200)^2 + 0.518(200) + 131.886
\][/tex]
3. Calculate each term separately:
- First, calculate [tex]\( 0.008 \times (200)^2 \)[/tex]:
[tex]\( (200)^2 = 40000 \)[/tex]
[tex]\( 0.008 \times 40000 = 320 \)[/tex]
- Then, calculate [tex]\( 0.518 \times 200 \)[/tex]:
[tex]\( 0.518 \times 200 = 103.6 \)[/tex]
4. Add these results to the constant term (131.886):
[tex]\[
y = 320 + 103.6 + 131.886
\][/tex]
5. Calculate the final result:
Add the numbers together:
[tex]\( y = 555.486 \)[/tex]
Based on these calculations, the predicted [tex]\( y \)[/tex]-value when [tex]\( x = 200 \)[/tex] is approximately 555.5, which matches option d.
Therefore, the answer is:
d. [tex]\( y = 555.5 \)[/tex]
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