General equation of the regression line x on y is ________.a.(x-xbar)=b_xy (y-ybar)b.(x-xbar)=b_yx (y-ybar)c.(x+xbar)=b_xy (y+ybar)d.(y-ybar)=b_xy (x-xbar)

To determine the general equation of the regression line $x$ on $y$, we must recall the correct formulation. The regression line expresses how one variable predicts another.

Breakdown of the Options

1. Option A: $(x - \overline{x}) = b_{xy} (y - \overline{y})$
2. Option B: $(x - \overline{x}) = b_{yx} (y - \overline{y})$
3. Option C: $(x + \overline{x}) = b_{xy} (y + \overline{y})$
4. Option D: $(y - \overline{y}) = b_{xy} (x - \overline{x})$

Relevant Concepts

The regression equation for predicting $x$ based on $y$ takes the form: $x = \overline{x} + b_{yx}(y - \overline{y})$ This can be rearranged to the form: $(x - \overline{x}) = b_{yx} (y - \overline{y})$

Analysis of Each Option

• Option A: Incorrect because it uses $b_{xy}$ instead of $b_{yx}$.
• Option B: Correct, as it correctly represents the equation for the regression of $x$ on $y$.
• Option C: Incorrect as it combines terms that do not align with regression format.
• Option D: Incorrect because it reflects the regression of $y$ on $x$.

Verify and Summarize

The only option that accurately represents the regression line $x$ on $y$ is Option B. In this case, $b_{yx}$ denotes the slope of the regression line, reflecting how changes in $y$ affect $x$.

Final Answer

The general equation of the regression line $x$ on $y$ is B. $(x - \overline{x}) = b_{yx} (y - \overline{y})$.