Thank you for visiting A construction manager is monitoring the progress of a new house build The scatterplot and table show the number of months since the start of. 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 determine which function best models the data, we need to find the relationship between the number of months since the start of the build (x) and the percentage of the house left to build (y). The data points provided are:
- Month 0: 100% left
- Month 1: 86% left
- Month 2: 65% left
- Month 3: 59% left
- Month 4: 41% left
- Month 5: 34% left
The relationship between these two variables appears to be linear, so we can use a linear regression model to represent this relationship in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
### Step-by-Step Solution
1. Identify the Variables:
- Independent variable (x): Number of months since the start of the build.
- Dependent variable (y): Percentage of the house left to build.
2. Determine the Slope (m) and Intercept (b):
- From the data, we can fit a line that best models this relationship.
- The slope [tex]\( m \)[/tex] represents the change in percentage left to build per month.
- The intercept [tex]\( b \)[/tex] represents the percentage of the house left at [tex]\( x = 0 \)[/tex].
3. Calculate Slope and Intercept:
- Through linear regression analysis, the calculated slope [tex]\( m \)[/tex] is approximately [tex]\(-13.46\)[/tex].
- The calculated intercept [tex]\( b \)[/tex] is approximately [tex]\(97.81\)[/tex].
4. Match the Function:
- Based on the calculations, the function that best matches the data is:
[tex]\[
y = -13.5x + 97.8
\][/tex]
- This function closely matches the given options and represents the decrease in the percentage of the house left to build as time progresses.
Thus, the correct choice among the given functions is [tex]\( y = -13.5x + 97.8 \)[/tex]. This linear function accurately models the relationship between the number of months since construction began and the percentage of the house still left to build.
- Month 0: 100% left
- Month 1: 86% left
- Month 2: 65% left
- Month 3: 59% left
- Month 4: 41% left
- Month 5: 34% left
The relationship between these two variables appears to be linear, so we can use a linear regression model to represent this relationship in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
### Step-by-Step Solution
1. Identify the Variables:
- Independent variable (x): Number of months since the start of the build.
- Dependent variable (y): Percentage of the house left to build.
2. Determine the Slope (m) and Intercept (b):
- From the data, we can fit a line that best models this relationship.
- The slope [tex]\( m \)[/tex] represents the change in percentage left to build per month.
- The intercept [tex]\( b \)[/tex] represents the percentage of the house left at [tex]\( x = 0 \)[/tex].
3. Calculate Slope and Intercept:
- Through linear regression analysis, the calculated slope [tex]\( m \)[/tex] is approximately [tex]\(-13.46\)[/tex].
- The calculated intercept [tex]\( b \)[/tex] is approximately [tex]\(97.81\)[/tex].
4. Match the Function:
- Based on the calculations, the function that best matches the data is:
[tex]\[
y = -13.5x + 97.8
\][/tex]
- This function closely matches the given options and represents the decrease in the percentage of the house left to build as time progresses.
Thus, the correct choice among the given functions is [tex]\( y = -13.5x + 97.8 \)[/tex]. This linear function accurately models the relationship between the number of months since construction began and the percentage of the house still left to build.
Thank you for reading the article A construction manager is monitoring the progress of a new house build The scatterplot and table show the number of months since the start of. 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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Rewritten by : Jeany
