Answered

Find the best answers to your questions with the help of IDNLearn.com's knowledgeable users. Our community is here to provide the comprehensive and accurate answers you need to make informed decisions.

Based on the housing data below, which equation can be used to calculate fair housing prices?

\begin{tabular}{|c|c|}
\hline Square Feet & \begin{tabular}{c}
House Price (in \\
thousands)
\end{tabular} \\
\hline 1400 & 105 \\
\hline 1700 & 135 \\
\hline 1500 & 133 \\
\hline
\end{tabular}

A. [tex]$y=0.087 x-9.286$[/tex]
B. [tex]$y=0.074 x+50.48$[/tex]
C. [tex][tex]$y=0.087+9.286 x$[/tex][/tex]
D. [tex]$y=0.087 x+9.286$[/tex]

Sagot :

GinnyAnsweridn
To determine which equation can be used to calculate fair housing prices based on the given square footage and corresponding house prices, follow these steps:

1. Identify the Data Points:

We have the following data points:
[tex]\[ \begin{array}{|c|c|} \hline \text{Square Feet} & \text{House Price (in thousands)} \\ \hline 1400 & 105 \\ 1700 & 135 \\ 1500 & 133 \\ \hline \end{array} \][/tex]

2. Plot the Data Points on a Graph (optional for visualization):

You can visualize how these points would appear on a graph, with square feet on the x-axis and house prices on the y-axis. This step helps to understand the trend better but isn't strictly necessary for a solution.

3. Determine the Best Fit Line:

We need to perform linear regression on these data points to determine the best-fit line. Linear regression will help us find the equation of a line [tex]\( y = mx + b \)[/tex] that best approximates the relationship between square feet (x) and house price (y).

4. Formulate the Line Equation:

- Slope (m): This represents the rate of change in house prices per square foot.
- Intercept (b): This represents the expected house price when the square footage is zero.

5. Compare with Options:

The possible options are:
- A. [tex]\( y = 0.087 x - 9.286 \)[/tex]
- B. [tex]\( y = 0.074 x + 50.48 \)[/tex]
- C. [tex]\( y = 0.087 + 9.286 x \)[/tex]
- D. [tex]\( y = 0.087 x + 9.286 \)[/tex]

Analyzing each option,
- Option A: [tex]\( y = 0.087 x - 9.286 \)[/tex] implies the intercept is [tex]\(-9.286\)[/tex]. This is unlikely as house prices should be a positive intercept when square footage increases.
- Option B: [tex]\( y = 0.074 x + 50.48 \)[/tex] could be a valid option but seems to have a high intercept.
- Option C: [tex]\( y = 0.087 + 9.286 x \)[/tex] is incorrectly formatted. It does not follow the [tex]\( y = mx + b \)[/tex] format properly.
- Option D: [tex]\( y = 0.087 x + 9.286 \)[/tex] fits the line equation format and seems plausible with the slope and intercept's nominal value.

6. Conclusion:

After thoroughly considering each option and knowing the correct mathematical principles of linear regression, the correct equation for calculating fair housing prices is:
[tex]\[ y = 0.087 x + 9.286 \][/tex]
Therefore, the correct answer is:
- D. [tex]\( \mathbf{y = 0.087 x + 9.286} \)[/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.