Question

the relationship between x = height of a student (in inches) and y = y number of steps required to walk the length of a school hallway is summarized with the regression line ŷ = 113.6 - 0.921x. for this model, technology gives s = 3.50 and r² = 0.399. interpret the value of r². about 39.9% of the variability in number of steps required to walk the length of a school hallway is accounted for by the least - squares regression line with x = height of a student (in inches). about 39.9% of number of steps required to walk the length of a school hallway is accounted for by the least - squares regression line with x = height of a student (in inches). there is a strong positive linear relationship between number of steps required to walk the length of a school hallway and height of a student (in inches). there is a weak positive linear relationship between number of steps required to walk the length of a school hallway and height of a student (in inches). about 39.9% of the variability in height of a student (in inches) is accounted for by the least - squares regression line with x = number of steps required to walk the length of a school hallway.

Explanation:

The coefficient of determination $r^{2}$ represents the proportion of the variance in the dependent - variable that is predictable from the independent variable. Here, the dependent variable is the number of steps ($y$) and the independent variable is the height of a student ($x$). A value of $r^{2}=0.399$ means that about 39.9% of the variability in the number of steps required to walk the length of a school hallway can be accounted for by the least - squares regression line with the height of a student as the predictor variable.

Answer:

A. About 39.9% of the variability in number of steps required to walk the length of a school hallway is accounted for by the least - squares regression line with $x$ = height of a student (in inches).