Question

5. Chapter 7: Exercise 68 on page 228

Birthrates 2015 The table shows the number of live births per 1000 women aged 15-44 years in the United States, starting in 1965.

Year	1965	1970	1975	1980	1985	1990	1995	2000	2005	2010	2015
Rate	19.4	18.4	14.8	15.9	15.6	16.4	14.8	14.4	14.0	13.0	12.4

A) Make a scatterplot and describe the general trend in Birth Rates (Enter Year as years since 1900: 65,70,75 etc.)

B) Find the equation of the regression of the line:

C) Check to see if the line is an appropriate model. Explain

D) Interpret the slope of the line

E) The table gives rates only at intervals. Estimate what the rate was in 1978

F) In 1978, the birthrate was actually 15.0. How close did your model come?

G) The birthrate in 2020 was not yet available when this was written. Predict the birth rate in 2020 from your model . Comment on your faith in this prediction.

H) Predict the Birthrate for 2050. Comment on your faith in this prediction.

Answer 1

A)

The above scatter plot has a trend which has the reduction of the birth rate with respect to time (year)

B) The regression equation is
Rate = 242.59 - 0.114 Year

C)

From the above graphs, we can assume that the assumption on the model is satisfied but it does not show a nice graph due to ness observation.

D) Interpret the slope of the line

Ans: The estimated value of the slope is -0.114. Therefore, for increasing 5 years decreases the birth rate by 0.114.

242.59 - 0.114 Year

E) The table gives rates only at intervals. Estimate what the rate was in 1978.

Ans: The estimated in 1978 was 16.743.

F) In 1978, the birthrate was actually 15.0. How close did your model come?

Ans: The estimated is greater (16.743-15)=1.743 than the actual birth rate.

G) The birthrate in 2020 was not yet available when this was written. Predict the birth rate in 2020 from your model . Comment on your faith in this prediction.

The predicted birth rate in 2020 using the model will be  11.947. It may be possible because of the change in the birth rate with respect to the year from the scatter plot.

H) Predict the Birthrate for 2050. Comment on your faith in this prediction.

The predicted birthrate in 2050 is  8.522. The chance of the wrong prediction by this model is high because during the coming 25 years there should be much change which can affect on the birth rate.