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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 :

GinnyAnswer
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]
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