When we use regression analysis,we are finding the regression equation that represents the geometrical line that comes closest to the distribution of points.This can be illustrated in which of the following?
A) the regression equation Y = a + bX allows us to infer values of X when we know the value of Y
B) the regression equation Y = a + bX allows us to infer values of Y when we know the value of X
C) the regression equation requires that we know the values of X, Y, a and b when we begin doing the analysis
D) the regression equation has little, if anything, to do with the understanding of the distribution of points in a data set

Question

Quizplus · Accepted Answer

The regression equation Y = a + bX allows us to infer values of Y when we know the value of X, meaning given the line of best fit (represented by the regression equation), we can estimate the value of Y for a given X value. This means that the regression equation represents the geometrical line that comes closest to the distribution of points in the scatter plot, as it is the line that minimizes the distance between the observed Y values and the predicted Y values based on the X values. Option A is incorrect, as the regression equation allows us to infer values of Y when we know the value of X, not the other way around. Option C is also incorrect, as the regression equation calculates the values of a and b as part of the analysis, so we do not need to know them beforehand. Option D is incorrect, as the regression equation is precisely about understanding and representing the distribution of points in the data set.

When We Use Regression Analysis,we Are Finding the Regression Equation