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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

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
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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