91Ó°ÊÓ

The given data is

A study was done to see if taller students needed fewer steps to go a certain distance. The scatterplot in the question depicts the link between height and the number of steps needed to walk down the school corridor.

As a result, we can see from the scatterplot that,

Because the scatterplot's pattern slopes downhill, the scatterplot's orientation is negative. Because there is no considerable curvature in the scatterplot, it takes the form of a linear graph. The scatterplot's strength is reasonably strong since the points in the scatterplot are not too close together but also not too far away.

The odd aspect is that no outliers occur since no points depart significantly from the pattern in the other points.

The given data is

A study was done to see if taller students needed fewer steps to go a certain distance. The scatterplot in the question depicts the link between height and the number of steps needed to walk down the school corridor. The least square regression line's general equation is:

$\hat{y}=b_0+b_{1}x$

As a result of the computer output, we can see that the constant estimate is presented in the row "Constant" and the column "Coef" as:

$b_0=113.57$

And the slope estimate is supplied in the row "Height" and the column "Coef" as follows:

$b_1=-0.9211$

Now we'll plug the above values into the regression line's equation, where $x$represents the height and $y$indicates the number of steps.

role="math" localid="1654242650804" $$\begin{gathered} \hat{y}=b_0+b_{1}x \\ =113.57-0.9211x. \end{gathered}$$

The given data is

A study was done to see if taller students needed fewer steps to go a certain distance. The scatterplot in the question depicts the link between height and the number of steps needed to walk down the school corridor. Now we must determine and interpret the value:

i) $b_0:$In the row "Constant" and the column "Coef" of the given computer output, the $y-$intercept $b_0$is presented as:

$b_0=113.57$

When $x$is zero, the $y-$intercept indicates the average $y-$value. When the height is 0 inches, the average number of steps is $113.57$steps.

ii. $b_1$: In the row "Height" and the column "Coef" of the given computer output, the slope $b_1$is given as:

$b_1=0.9211$

The slope shows how much y has increased or decreased per unit of $x$. As a result, the average number of steps is $-0.9211$less than the actual number of steps.

iii. $s$: the standard error of the estimate $s$ is supplied in the computer output after " $S=$" as:

$s=3.50429$

As a result, the anticipated number of steps differs by $3.50429$steps on average from the actual number of steps.

iv. $SE{b}_1:$In the row "Height" and the column "SE Coef" of the given computer output, the standard error of the slope $SE{b}_1$is presented as:

$SE{b}_1=0.1938$

As a result, the slope of the sample regression line differs from the true population regression line by $0.1938$on average.