Question

# The intercept a describes? A). The amount variance accounted for B). The estimated difference in response...

The intercept a describes?

A). The amount variance accounted for
B). The estimated difference in response variable (y) if the explanatory variable (x) is one unit larger.
C). The correlation between x and y.
D). The average outcome when the explanatory variable (x) is equal to zero.

we know that the regression equation is y = a + bx

where a is intercept and b is slope.

when we put x = 0, then we have the following equation , y = a + b*0 = a +0 = a

so, the intercept is the outcome when the explanatory variable x is equal to 0

thus, only option D is correct.

option A is incorrect because b never account for variance

option B is incorrect because we can't find out the value of b when the x value is one unit as the equation becomes y = a + b*1 = a+b, so this is an equation of a and b, but not only a

option C is incorrect because the correlation between x and y is denoted by r which is not a part of the regression equation.

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