Question

the scatter plot and trend line show the average income, in dollars, in several major american cities plotted against the rent for a 2-bedroom apartment in those cities. assuming the line correctly models the trend in the data, what does this line’s slope of 0.031 mean? choose 1 answer: (a) the average house for rent is 0.031 million square feet. (b) the average rent was 0.031 thousand dollars. (c) on average, each $1 increase in average income was associated with a $0.031 increase in average rent. (d) on average, each $0.031 increase in average income was associated with a 1 point increase in average rent.

Explanation:

To determine the meaning of the slope, recall that in a linear model \( y = mx + b \), the slope \( m \) represents the change in \( y \) per unit change in \( x \). Here, the \( x \)-axis is average income (in dollars) and the \( y \)-axis is rent (in dollars). The slope is \( 0.031 \), so for each \( \$1 \) increase in average income (\( x \)), the rent (\( y \)) increases by \( \$0.031 \).

• Option A is incorrect because slope does not relate to square footage.
• Option B is incorrect as it misinterprets the slope as a rent value, not a rate of change.
• Option D is incorrect because it reverses the relationship and misinterprets the units.

Answer:

C. On average, each $1 increase in average income was associated with a $0.031 increase in average rent.