The paired data below consists of heights and weights of 6 randomly selected adults. The equation of the regression line is $\hat { y } = - 181.342 + 144.46 \mathrm { x }$. Find the standard error of estimate.
$\begin{array}{c|rrrrrr}
\text { x Height (meters) } & 1.61 & 1.72 & 1.78 & 1.80 & 1.67 & 1.88 \
\hline \mathrm{y} \text { Weight }(\mathrm{kg}) & 54 & 62 & 70 & 84 & 61 & 92
\end{array}$
A) $5.0015$
B) $15.648$
C) $6.9205$
D) $9.7944$

Question

Quizplus · Accepted Answer

The standard error of estimate is the square root of the mean squared error, which is the average of the squared differences between the observed values and the predicted values. The mean squared error is calculated as:$$MSE = \frac{1}{n} \sum_{i=1}^n (y_i - \hat{y}_i)^2$$where $y_i$ is the observed value, $\hat{y}_i$ is the predicted value, and $n$ is the number of observations.In this case, we have:$$MSE = \frac{1}{6} \sum_{i=1}^6 (y_i - \hat{y}_i)^2$$$$= \frac{1}{6} [(54 - (-181.342 + 144.46 \times 1.61))^2 + (62 - (-181.342 + 144.46 \times 1.72))^2 + (70 - (-181.342 + 144.46 \times 1.78))^2 + (84 - (-181.342 + 144.46 \times 1.80))^2 + (61 - (-181.342 + 144.46 \times 1.67))^2 + (92 - (-181.342 + 144.46 \times 1.88))^2]$$$$= 5.0015$$Therefore, the standard error of estimate is $5.0015$.

The Paired Data Below Consists of Heights and Weights of 6