Fitting a straight line to a set of data yields the following prediction line. C

Question

Fitting a straight line to a set of data yields the following prediction line. Complete (a) through (c) below.

ModifyingAbove Upper Y with caret Subscript i =10+2Xi

Interpret the meaning of the Y-intercept,

b 0

e correct answer below.

A.

The Y-intercept,

b 0

=2,

implies that when the value of X is 0, the mean value of Y is 2

B.

The Y-intercept,

b 0 =10,

implies that when the value of X is 0, the mean value of Y is 10.

C.

The Y-intercept,

b 0 =10,

implies that for each increase of 1 unit in X, the value of Y is expected to increase by

10

units.

D.

The Y-intercept,

b 0 =10,

implies that the average value of Y is 10.

Interpret the meaning of the slope, b 1

Predict the mean value of Y for Upper X =4.

Explanation / Answer

The regression equation is

Yi =10+2Xi

Interpret the meaning of the Y-intercept,

The correct answer is

The Y-intercept,

B. b0 =10, implies that when the value of X is 0, the mean value of Y is 10.

Interpret the meaning of the slope, b 1

b1 = 2, implies that for each increase of 1 unit in X, the value of Y is expected to increase by 2

Predict the mean value of Y for Upper X =4.

Yi =10+2 * 4 = 18

So, the mean value of Y for X = 4 is 18

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