Thank you for visiting The following table of values gives a company s annual profits in millions of dollars Rescale the data so that the year 2003 corresponds to. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To find the cubic regression model for the given data and identify the coefficient of the [tex]\(x^2\)[/tex] term, we should go through the following steps:
1. Rescale the Data:
First, we need to adjust the years so that the year 2003 corresponds to [tex]\(x = 0\)[/tex]. This means we assign each year a value relative to the year 2003.
- Year 2003 becomes [tex]\(x = 0\)[/tex].
- Year 2004 becomes [tex]\(x = 1\)[/tex].
- Year 2005 becomes [tex]\(x = 2\)[/tex].
- Year 2006 becomes [tex]\(x = 3\)[/tex].
- Year 2007 becomes [tex]\(x = 4\)[/tex].
- Year 2008 becomes [tex]\(x = 5\)[/tex].
2. Record the Profits:
We have the profits corresponding to these years:
- 2003: 31.3 million dollars
- 2004: 32.7 million dollars
- 2005: 31.8 million dollars
- 2006: 33.7 million dollars
- 2007: 35.9 million dollars
- 2008: 36.1 million dollars
3. Fit a Cubic Regression Model:
The goal here is to fit a cubic polynomial model of the form:
[tex]\[
y = ax^3 + bx^2 + cx + d
\][/tex]
We would use the rescaled [tex]\(x\)[/tex] values (0, 1, 2, 3, 4, 5) and the corresponding profits to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex].
4. Identify the Coefficient for [tex]\(x^2\)[/tex]:
Once the cubic regression is computed, we examine the coefficients to find the one associated with the [tex]\(x^2\)[/tex] term.
The coefficient of the [tex]\(x^2\)[/tex] term is [tex]\(0.5310\)[/tex].
Therefore, the answer to the question of which number is the coefficient of the [tex]\(x^2\)[/tex] term of the cubic regression model is [tex]\(0.5310\)[/tex].
1. Rescale the Data:
First, we need to adjust the years so that the year 2003 corresponds to [tex]\(x = 0\)[/tex]. This means we assign each year a value relative to the year 2003.
- Year 2003 becomes [tex]\(x = 0\)[/tex].
- Year 2004 becomes [tex]\(x = 1\)[/tex].
- Year 2005 becomes [tex]\(x = 2\)[/tex].
- Year 2006 becomes [tex]\(x = 3\)[/tex].
- Year 2007 becomes [tex]\(x = 4\)[/tex].
- Year 2008 becomes [tex]\(x = 5\)[/tex].
2. Record the Profits:
We have the profits corresponding to these years:
- 2003: 31.3 million dollars
- 2004: 32.7 million dollars
- 2005: 31.8 million dollars
- 2006: 33.7 million dollars
- 2007: 35.9 million dollars
- 2008: 36.1 million dollars
3. Fit a Cubic Regression Model:
The goal here is to fit a cubic polynomial model of the form:
[tex]\[
y = ax^3 + bx^2 + cx + d
\][/tex]
We would use the rescaled [tex]\(x\)[/tex] values (0, 1, 2, 3, 4, 5) and the corresponding profits to determine the coefficients [tex]\(a\)[/tex], [tex]\(b\)[/tex], [tex]\(c\)[/tex], and [tex]\(d\)[/tex].
4. Identify the Coefficient for [tex]\(x^2\)[/tex]:
Once the cubic regression is computed, we examine the coefficients to find the one associated with the [tex]\(x^2\)[/tex] term.
The coefficient of the [tex]\(x^2\)[/tex] term is [tex]\(0.5310\)[/tex].
Therefore, the answer to the question of which number is the coefficient of the [tex]\(x^2\)[/tex] term of the cubic regression model is [tex]\(0.5310\)[/tex].
Thank you for reading the article The following table of values gives a company s annual profits in millions of dollars Rescale the data so that the year 2003 corresponds to. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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