Compute the intercept of the regression line for the data below.
$\begin{array}{cccc}
\mathrm{X} \text { values } & -3 & 0 & 6 \
\mathrm{Y} \text { values } & 6 & 5 & -2
\end{array}$

A) 0.71
B) 3.72
C) 3.93
D) 9.32

Question

Compute the intercept of the regression line for the data below. 
$\begin{array}{cccc}
\mathrm{X} \text { values } & -3 & 0 & 6 \
\mathrm{Y} \text { values } & 6 & 5 & -2
\end{array}$

A) 0.71
B) 3.72
C) 3.93
D) 9.32

Quizplus · Accepted Answer

To find the intercept of the regression line, we need to calculate the slope and the y-intercept of the line using the formula: $b=\bar{y}-m\bar{x}$, where $b$ is the y-intercept and $m$ is the slope of the line.

First, we need to calculate the mean of X and Y values:
$\bar{x} = \frac{-3+0+6}{3} = \frac{3}{3} = 1$
$\bar{y} = \frac{6+5+(-2)}{3} = \frac{9}{3} = 3$

To find the slope, we use the formula 
$m = \frac{\sum_{i=1}^n (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^n (x_i - \bar{x})^2}$

Plugging in the values, we get
$m = \frac{(-4)(3) + (1)(2) + (5)(-5)}{(-4)^2 + 1^2 + 5^2} = -\frac{17}{42}$

Now, we can find the y-intercept $b=\bar{y}-m\bar{x}$:
$b = 3 - (-\frac{17}{42})(1) = \frac{131}{42} \approx 3.93$

Therefore, the answer is C.

Compute the Intercept of the Regression Line for the Data X values −306Y values 65−2\begin{array}{cccc}\mathrm{X} \text { values } & -3 & 0 & 6 \\\mathrm{Y} \text { values } & 6 & 5 & -2\end{array}X values Y values ​−36​05​6−2​

Compute the Intercept of the Regression Line for the Data $\begin{array}{cccc}\mathrm{X} \text { values } & -3 & 0 & 6 \\\mathrm{Y} \text { values } & 6 & 5 & -2\end{array}$