8.- The scatterplot and the model compares the years and the median square footage of newly built homes. Years versus Square Footages a) { Use the linear model to estimate the median square footage of house built in 1985 2600 2400 Find the actual mean square footage of a b. house built in 1985 2200
8.- The scatterplot and the model compares the years and the median square footage of newly built homes. Years versus Square Footages a) { Use the linear model to estimate the median square footage of house built in 1985 2600 2400 Find the actual mean square footage of a b. house built in 1985 2200
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter8: Linear Functions
Section8.6: Writing Linear Equations
Problem 33E
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![### Understanding Linear Models with Real Estate Data
#### Analyzing Median Square Footage of Newly Built Homes Over Time
**8. The scatterplot and the model compare the years and the median square footage of newly built homes.**
- **Scatterplot Details:**
- **X-Axis (Horizontal):** Represents the years ranging from 1980 to 2015.
- **Y-Axis (Vertical):** Represents the median square footage of newly built homes, ranging from 1400 to 2600 square feet.
- **Data Points:** Blue dots on the scatterplot represent actual data points for the median square footage in different years.
- **Linear Model:** A red line represents the linear model that approximates the relationship between the year and the median square footage.
**Questions:**
a) **Use the linear model to estimate the median square footage of a house built in 1985.**
b) **Find the actual mean square footage of a house built in 1985.**
c) **Find the error in the estimation.**
d) **Is the linear model overestimating or underestimating the mean square footage?**
---
#### Detailed Explanation and Walkthrough
**a) Estimating Median Square Footage for 1985:**
- To estimate the median square footage for a house built in 1985 using the linear model, find where the year 1985 intersects with the red line on the scatterplot.
- From the graph, locate the corresponding value on the Y-Axis (median square footage) that aligns with this intersection.
**b) Actual Median Square Footage for 1985:**
- Identify the blue data point corresponding to the year 1985 on the scatterplot.
- From the graph, the actual median square footage for a house built in 1985 can be approximated based on the Y-Axis value at that data point.
**c) Finding the Error in Estimation:**
- Calculate the difference between the estimated value (from part a) and the actual value (from part b).
**d) Determining the Accuracy of the Linear Model:**
- Compare the estimated value and the actual value to see if the linear model is overestimating or underestimating the median square footage.
- If the estimated value is higher than the actual value, the model is overestimating.
- Conversely, if the estimated value is lower, the model is underestimating.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4cc8d8-0cf8-4dd0-a514-815d4b227054%2Fb26a0b36-c909-4162-bc28-6e7c864e3a77%2F2goxyih_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Linear Models with Real Estate Data
#### Analyzing Median Square Footage of Newly Built Homes Over Time
**8. The scatterplot and the model compare the years and the median square footage of newly built homes.**
- **Scatterplot Details:**
- **X-Axis (Horizontal):** Represents the years ranging from 1980 to 2015.
- **Y-Axis (Vertical):** Represents the median square footage of newly built homes, ranging from 1400 to 2600 square feet.
- **Data Points:** Blue dots on the scatterplot represent actual data points for the median square footage in different years.
- **Linear Model:** A red line represents the linear model that approximates the relationship between the year and the median square footage.
**Questions:**
a) **Use the linear model to estimate the median square footage of a house built in 1985.**
b) **Find the actual mean square footage of a house built in 1985.**
c) **Find the error in the estimation.**
d) **Is the linear model overestimating or underestimating the mean square footage?**
---
#### Detailed Explanation and Walkthrough
**a) Estimating Median Square Footage for 1985:**
- To estimate the median square footage for a house built in 1985 using the linear model, find where the year 1985 intersects with the red line on the scatterplot.
- From the graph, locate the corresponding value on the Y-Axis (median square footage) that aligns with this intersection.
**b) Actual Median Square Footage for 1985:**
- Identify the blue data point corresponding to the year 1985 on the scatterplot.
- From the graph, the actual median square footage for a house built in 1985 can be approximated based on the Y-Axis value at that data point.
**c) Finding the Error in Estimation:**
- Calculate the difference between the estimated value (from part a) and the actual value (from part b).
**d) Determining the Accuracy of the Linear Model:**
- Compare the estimated value and the actual value to see if the linear model is overestimating or underestimating the median square footage.
- If the estimated value is higher than the actual value, the model is overestimating.
- Conversely, if the estimated value is lower, the model is underestimating.
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