High School

We appreciate your visit to A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

A construction manager is monitoring the progress of building a new house. The scatterplot and table show the number of months since the start of the build and the percentage of the house still left to build. A linear function can be used to model this relationship.

**New House Progress**

\[
\begin{array}{|c|c|}
\hline
\text{Months Since Start (x)} & \text{Percentage of House Left to Build (y)} \\
\hline
0 & 200 \\
\hline
1 & 90 \\
\hline
3 & 65 \\
\hline
4 & 41 \\
\hline
5 & 34 \\
\hline
\end{array}
\]

Which function best models the data?

A. [tex]y = -13.5x + 97.8[/tex]
B. [tex]y = -13.5x + 7.3[/tex]
C. [tex]y = 97.8x - 13.5[/tex]
D. [tex]y = 7.3x - 97.8[/tex]

Select one:
- [ ] A
- [ ] B
- [ ] C
- [ ] D

Answer :

To find the linear function that best models the data provided in the table, we need to evaluate the given functions and determine which one fits the data points more accurately. Here's how the process works:

1. Data Points:
- We have the following data points regarding the number of months since the start and the percentage of the house left to build:
- (0, 200)
- (3, 65)
- (3, 99)
- (4, 41)
- (5, 34)

Note: The data point where x = 1 does not have a y-value, so we exclude it from analysis.

2. Possible Linear Models:
- We are given four possible linear models to consider:
- [tex]\( y = -13.5x + 97.8 \)[/tex]
- [tex]\( y = -13.5x + 7.3 \)[/tex]
- [tex]\( y = 97.8x - 13.5 \)[/tex]
- [tex]\( y = 7.3x - 97.8 \)[/tex]

3. Determine Fit:
- We calculate how well each model fits the data points by evaluating the predicted y-values from each model and comparing them to the actual y-values.
- The method used to find the best fit is by calculating the Sum of Squared Differences (SSD) between the actual and predicted values for the given data points.

4. Comparison Results:
- The model: [tex]\( y = -13.5x + 97.8 \)[/tex] resulted in an SSD of 12,264.55.
- The model: [tex]\( y = -13.5x + 7.3 \)[/tex] resulted in an SSD of 80,818.30.
- The model: [tex]\( y = 97.8x - 13.5 \)[/tex] resulted in an SSD of 432,778.21.
- The model: [tex]\( y = 7.3x - 97.8 \)[/tex] resulted in an SSD of 160,221.91.

5. Conclusion:
- The linear model that provides the best fit, with the smallest SSD, is [tex]\( y = -13.5x + 97.8 \)[/tex].

Therefore, the function [tex]\( y = -13.5x + 97.8 \)[/tex] best models the relationship between the number of months and the percentage of the house left to build.

Thanks for taking the time to read A construction manager is monitoring the progress of building a new house The scatterplot and table show the number of months since the start of. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada