Question

Use a graphing utility to find the regression curves specified. The median price of single-family homes in the United States increased quite consistently during the years 1976-2000. Then a housing "bubble" occurred for the years $2001-2010,$ in which prices first rose dramatically for 6 years and then dropped in a steep "crash" over the next 4 years, causing considerable turmoil in the U.S. economy. The table shows some of the data as reported by the National Association of Realtors. $$\begin{array}{lc|cc}\hline \text { Year } & \text { Price (\$) } & \text { Year } & \text { Price (\$) } \\\hline 1976 & 37400 & 2000 & 122600 \\1980 & 56250 & 2002 & 150000 \\1984 & 66500 & 2004 & 187500 \\1988 & 87500 & 2006 & 247500 \\1992 & 95800 & 2008 & 183300 \\1996 & 104200 & 2010 & 162500 \\\hline\end{array}$$ a. Make a scatterplot of the data. b. Find and plot the regression line for the years $1976-2002$ and superimpose the line on the scatterplot in part (a). c. How would you interpret the meaning of a data point in the housing "bubble"?

   Use a graphing utility to find the regression curves specified.
The median price of single-family homes in the United States increased quite consistently during the years 1976-2000. Then a housing "bubble" occurred for the years $2001-2010,$ in which prices first rose dramatically for 6 years and then dropped in a steep "crash" over the next 4 years, causing considerable turmoil in the U.S. economy. The table shows some of the data as reported by the National Association of Realtors.
$$\begin{array}{lc|cc}\hline \text { Year } & \text { Price (\$) } & \text { Year } & \text { Price (\$) } \\\hline 1976 & 37400 & 2000 & 122600 \\1980 & 56250 & 2002 & 150000 \\1984 & 66500 & 2004 & 187500 \\1988 & 87500 & 2006 & 247500 \\1992 & 95800 & 2008 & 183300 \\1996 & 104200 & 2010 & 162500 \\\hline\end{array}$$
a. Make a scatterplot of the data.
b. Find and plot the regression line for the years $1976-2002$ and superimpose the line on the scatterplot in part (a).
c. How would you interpret the meaning of a data point in the housing "bubble"?

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Thomas Calculus in SI Units

Thomas Calculus in SI Units

George B. Thomas,… 13th Edition

Chapter 1, Problem 39

Instant Answer

Solved by Expert Carson Merrill

10/27/2023

Step 1

To make a scatterplot of the data, plot the points with the years on the x-axis and the prices on the y-axis. You should see a general upward trend in the data, with a sharp increase in prices during the housing bubble years. b. Show more…

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Use a graphing utility to find the regression curves specified. The median price of single-family homes in the United States increased quite consistently during the years 1976-2000. Then a housing "bubble" occurred for the years $2001-2010,$ in which prices first rose dramatically for 6 years and then dropped in a steep "crash" over the next 4 years, causing considerable turmoil in the U.S. economy. The table shows some of the data as reported by the National Association of Realtors. $$\begin{array}{lc|cc}\hline \text { Year } & \text { Price (\$) } & \text { Year } & \text { Price (\$) } \\\hline 1976 & 37400 & 2000 & 122600 \\1980 & 56250 & 2002 & 150000 \\1984 & 66500 & 2004 & 187500 \\1988 & 87500 & 2006 & 247500 \\1992 & 95800 & 2008 & 183300 \\1996 & 104200 & 2010 & 162500 \\\hline\end{array}$$ a. Make a scatterplot of the data. b. Find and plot the regression line for the years $1976-2002$ and superimpose the line on the scatterplot in part (a). c. How would you interpret the meaning of a data point in the housing "bubble"?

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Key Concepts

Scatterplot

A scatterplot is a graphical representation that displays data points on a coordinate plane, with one variable plotted along the horizontal axis and another along the vertical axis, enabling visual identification of patterns, trends, or anomalies in the relationship between the variables.

Regression Analysis

Regression analysis involves determining the best-fitting line or curve through a set of data points to model the relationship between an independent variable and a dependent variable. This process minimizes the prediction errors and helps in understanding trends, making predictions, or identifying underlying relationships within the data.

Outlier Analysis

Outlier analysis focuses on understanding data points that deviate significantly from the trend captured by the regression model. In contexts such as a housing bubble, individual data points that fall far from the established trend may represent extraordinary events or market anomalies, and analyzing them helps in assessing model limitations and the impact of unusual circumstances.

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