Question

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

Yi=16−0.3Xi

a. Interpret the meaning of the​ Y-intercept,b0 Choose the correct answer below.

1. The​ Y-intercept, b0 =16​, implies that when the value of X is​ 0, the mean value of Y is 16.
2. The​ Y-intercept, b0=−0.3​, implies that when the value of X is​ 0, the mean value of Y is −0.3.
3. The​ Y-intercept, b0=16​, implies that the average value of Y is 16.
4. The​ Y-intercept, b0=16​, implies that for each increase of 1 unit in​ X, the value of Y is expected to increase by 16 units.

b. Interpret the meaning of the​ slope, b1. Choose the correct answer below.

1. The​ slope, b1=0.3​, implies that for each increase of 1 unit in​ X, the value of Y is expected to increase by 0.3 units.
2. The​ slope, b1=−0.3​, implies that for each increase of 1 unit in​ X, the value of Y is estimated to decrease by 0.3 units.
3. The​ slope, b1=−0.3​, implies that the average value of Y is −0.3
4. The​ slope, b1=16​, implies that for each increase of 1 unit in​ X, the value of Y is expected to increase by 16 units.

c. Predict the mean value of Y for X=6.

Yi=

​(Type an integer or a​ decimal.)

Answer 1

Here

Yi=16−0.3Xi

a. Here we need to interpret the meaning of Y-intercept, b0

Here we see that b0=16, which means for X=0, value of Y is 16

Hence answer is

A. The​ Y-intercept, b0 =16​, implies that when the value of X is​ 0, the mean value of Y is 16.

b. Here we need to interpret the meaning of the slope b1

Here we see that b1=-0.3, which means there is decreasing trend in the model. Which means for every increase in X, Y decreases by -0.3.

Hence the answer is

B. The​ slope, b1=−0.3​, implies that for each increase of 1 unit in​ X, the value of Y is estimated to decrease by 0.3 units.

c.Now we know that Yi=16-0.3Xi

Now for X=6, Yi=16-0.3*6=14.2