Question

In a simple linear regression, the following sample regression equation is obtained:

yˆ=407−21x.y^=407−21x.

a.

Interpret the slope coefficient.

	As x increases by 1 unit, y is predicted to decrease by 21 units.
	As x increases by 1 unit, y is predicted to increase by 21 units.
	As x increases by 1 unit, y is predicted to decrease by 407 units.
	As x increases by 1 unit, y is predicted to increase by 407 units.

b.	Predict y if x equals −27.

yˆy^

Answer 1

(a) = 407 - 21x, which is of the form = a + bx, where a is the y intercept, and b is the slope of the line.

Here the slope is negative, which means that as x increases, y will decrease (and vice versa in the opposite direction).

when x = 1, = 407 - (21 * 1) = 386

when x = 2, = 407 - (21 * 2) = 365

We see that as x increased by 1, decreased by 386 - 365 = 21

Therefore Option 1: As x increases by 1 unit, y is predicted to decrease by 21 units.

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(b) When x = -27, = 407 - (21 * -27) = 407 + 567

Therefore = 974

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