The scatterplot above shows the relative housing cost and...

The scatterplot above shows the relative housing cost and the population density for several large US cities in the year $2005 .$ The line of best fit is also shown and has equation $y=0.0125 x+61 .$ Which of the following best explains how the number 61 in the equation relates to the scatterplot? A) In $2005,$ the lowest housing cost in the United States was about $\$ 61$ per month. B) In $2005,$ the lowest housing cost in the United States was about 61$\%$ of the highest housing cost. C) In $2005,$ even in cities with low population densities, housing costs were nelow 61$\%$ of the national average. D) In 2005 , even in cities with low poulation densities, housing costs were likely at least 61$\%$ of the national average.

The scatterplot above shows the relative housing cost and the population density for several large US cities in the year
$2005 .$ The line of best fit is also shown and has equation $y=0.0125 x+61 .$ Which of the following best explains how
the number 61 in the equation relates to the scatterplot?
A) In $2005,$ the lowest housing cost in the United States was about $\$ 61$ per month.
B) In $2005,$ the lowest housing cost in the United States was about 61$\%$ of the highest housing cost.
C) In $2005,$ even in cities with low population densities, housing costs were nelow 61$\%$ of the national average.
D) In 2005 , even in cities with low poulation densities, housing costs were likely at least 61$\%$ of the national average.

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Key Concepts

Y-Intercept

The y-intercept is the constant term in the linear equation, representing the predicted value of the dependent variable when the independent variable is zero. In a scatterplot analysis, it provides a baseline estimate, indicating what value of the dependent variable one might expect when the independent variable is at its minimal or zero level.

Interpretation of Regression Parameters

Interpreting regression parameters involves understanding both the slope and the y-intercept in the context of the data. The slope indicates the rate of change of the dependent variable with respect to the independent variable, while the y-intercept offers insight into the starting or baseline value, which is crucial for understanding the overall trend illustrated by the scatterplot.

Linear Regression

Linear regression is a statistical method used to model the relationship between a dependent variable and an independent variable by fitting a best?fit straight line through a set of data points. This method helps in predicting the value of the dependent variable based on the value of the independent variable.

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