$$\begin{array}{l}
\text { Compute the standard error of the estimate for the data below. Round to the thousandths } 1\
\begin{array} { c | c c c c c c }
x & 27 & 28 & 29 & 30 & 31 & 32 \
\hline y & 116.95 & 120.37 & 125.26 & 124.90 & 129.37 & 130.90
\end{array}
\end{array}$$
A) 1.291
B) 1.510
C) 1.289
D) 1.057

Question

$$\begin{array}{l}
\text { Compute the standard error of the estimate for the data below. Round to the thousandths } 1\
\begin{array} { c | c c c c c c } 
x & 27 & 28 & 29 & 30 & 31 & 32 \
\hline y & 116.95 & 120.37 & 125.26 & 124.90 & 129.37 & 130.90
\end{array}
\end{array}$$
A) 1.291
B) 1.510
C) 1.289
D) 1.057

Quizplus · Accepted Answer

To compute the standard error of the estimate, we first need to find the regression line (least squares line) and then use the formula for the standard error of the estimate, which is $\sqrt{\frac{\sum(y_i - \hat{y}_i)^2}{n-2}}$, where $y_i$ are the observed values, $\hat{y}_i$ are the predicted values from the regression line, and $n$ is the number of observations.1. Calculate the means of $x$ and $y$: $\bar{x} = \frac{27+28+29+30+31+32}{6} = 29.5$, $\bar{y} = \frac{116.95+120.37+125.26+124.90+129.37+130.90}{6} = 124.625$.2. Calculate the slope ($b$) of the regression line: $b = \frac{\sum(x_i - \bar{x})(y_i - \bar{y})}{\sum(x_i - \bar{x})^2}$.3. Calculate the intercept ($a$) of the regression line: $a = \bar{y} - b\bar{x}$.4. Calculate the predicted values ($\hat{y}_i$) using the regression line equation $\hat{y} = a + bx$.5. Calculate the sum of squared residuals ($\sum(y_i - \hat{y}_i)^2$).6. Finally, calculate the standard error of the estimate using the formula given above.Given the complexity of these calculations and the lack of intermediate steps provided, the correct answer is determined by performing these calculations, which results in a standard error of the estimate close to 1.289, making option C the correct choice.

A) 1291 B) 1

A) 1291
B) 1