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Answer :
To estimate a fair price for a 1700 ft² home using linear regression based on the given housing data, we can follow these steps:
1. Understand the Data: We have data for three homes with their respective square footage and prices (in thousands of dollars):
- 2156 square feet: [tex]$210,000
- 2040 square feet: $[/tex]200,000
- 2050 square feet: [tex]$204,000
2. Set Up the Equation: Linear regression helps us find a straight line (equation) that best fits our data. The equation of a line is generally given by:
\[
\text{Price} = (\text{slope} \times \text{Square Feet}) + \text{intercept}
\]
3. Calculate the Slope and Intercept: For the data above, when calculating using linear regression methods, we determine:
- Slope: Approximately \(0.0741\)
- Intercept: Approximately \(50.48\)
4. Estimate the Price for 1700 ft²: With the slope and intercept values, we substitute into the linear equation to find the estimated price for a 1700 ft² home:
\[
\text{Estimated Price} = (0.0741 \times 1700) + 50.48
\]
5. Perform the Calculation:
- Multiply the slope (\(0.0741\)) by 1700 to get approximately \(125.97\).
- Add the intercept (\(50.48\)) to \(125.97\), giving an estimated price of approximately \(176.45\).
6. Convert the Price to Thousands: Since the prices in the data are in thousands, the estimated price in thousands is approximately \(176\).
7. Find the Closest Option: Among the given options, the closest estimated price for a 1700 ft² home is option B, which is \(\$[/tex]176,000\).
Conclusion: The estimated fair price for a 1700 ft² home is approximately [tex]$176,000. So, the correct answer is B. \$[/tex]176,000.
1. Understand the Data: We have data for three homes with their respective square footage and prices (in thousands of dollars):
- 2156 square feet: [tex]$210,000
- 2040 square feet: $[/tex]200,000
- 2050 square feet: [tex]$204,000
2. Set Up the Equation: Linear regression helps us find a straight line (equation) that best fits our data. The equation of a line is generally given by:
\[
\text{Price} = (\text{slope} \times \text{Square Feet}) + \text{intercept}
\]
3. Calculate the Slope and Intercept: For the data above, when calculating using linear regression methods, we determine:
- Slope: Approximately \(0.0741\)
- Intercept: Approximately \(50.48\)
4. Estimate the Price for 1700 ft²: With the slope and intercept values, we substitute into the linear equation to find the estimated price for a 1700 ft² home:
\[
\text{Estimated Price} = (0.0741 \times 1700) + 50.48
\]
5. Perform the Calculation:
- Multiply the slope (\(0.0741\)) by 1700 to get approximately \(125.97\).
- Add the intercept (\(50.48\)) to \(125.97\), giving an estimated price of approximately \(176.45\).
6. Convert the Price to Thousands: Since the prices in the data are in thousands, the estimated price in thousands is approximately \(176\).
7. Find the Closest Option: Among the given options, the closest estimated price for a 1700 ft² home is option B, which is \(\$[/tex]176,000\).
Conclusion: The estimated fair price for a 1700 ft² home is approximately [tex]$176,000. So, the correct answer is B. \$[/tex]176,000.
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