Question

2. Choose a country and research population data in order to fill out the table belo

a. Copy the population numbers counted each five years, as shown in the data base, for the years from 1950 to 2000 . Add a column, \(t\), measuring years șince 1945 .

b. What is the country you selected? In what part of the world is it? What is the magnitude of its population numbers? \(\left(100,000^{\circ} \mathrm{s}\right.\), millions, hundred millions, billions?) Is it growing or shrinking in population size?

c. Enter years since 1945 and your population numbers into your graphing calculator. Create a scatterplot of the data. Is the data growing or shrinking? Does it appear to be a linear pattern or non-linear? Explain your conclusions.

d. Use your calculator to fit a linear model to the population size.

i. Write the equation of the linear regression and superimpose its graph on your scatterplot.

ii. Use TI-Connect to copy the scatterplot onto your write-up, or just draw a sketch of it.

iii. How well does the linear model fit your data?

iv. What is the vertical intercept of the regression model? What does it mean in the context of the population?

v. What is the slope of the regression model? What does it mean in the context of the population?

vi. Use the model to predict the population size in the year you were born. Also, use the model to predict the population size in the year \(2007 .\)

e. Next fit an exponential model to your population data.

i. Write the equation of the exponential regression and superimpose its graph on your scatterplot.

ii. How well does the exponential model fit your data? By looking at the graphs, does it appear that the exponential model fits better than the linear model?

iii. What is the exponential factor in your model? What does it mean in the context of the population?

f. Experiment with some of the other regression models we have covered in class, and pick one of them to explain your population data. Write a paragraph explaining which regression model you feel best explains the population changes in your country.

Answer 1

We wll find an equation of the regression line in 4 steps ep 1: Find X·Yand Xe as it was done in the table below 20 25 30 35 40 45 50 10042 10709 11449 12248 13002 13683 14148 14514 14966 15468 15926 50210 107090 171735 244960 325050 410490 495180 580560 673470 773400 875930 25 100 225 400 625 900 1225 1600 2025 2500 3025 Step 2: Find the sum of every column: X-330. 〉Y-146155, 〉,X,Y-4708075. 〉,X"-12650 Step 3: Use the following equations to find a and b ΣΥ. Σ z? _ ΣΧ. ΣΧΥ 146155 . 12650-330 . 4708075 9758.545 11 12650 -3302 n·5) XY-5X-5 Y 11-4708075 _ 330-140155 11 12650 (330)2 Step 4: Substitute a and b in regression equation formula У 9758.545 + 117.609.

equation of the regression line is y=9758.545+117.609x

slope = 117.609

I was born in the Year 1993 so x=48

Y=9758.545+117.609*48=15403.777

Step 1: Find X.Y.X2 and Y2 as it was done in the table below 20 25 30 35 40 45 50 10042 10709 11449 12248 13002 13683 14148 14514 14966 15468 15926 X.Y 50210 107090 171735 244960 325050 410490 495180 580560 673470 773400 875930 25 100 225 400 625 900 1225 1600 2025 Y.Y 100841764 114682681 131079601 150013504 169052004 187224489 200165904 210656196 223981156 239259024 253637476 3025 Step 2: Find the sum of every column to get: ΣΧ-330, ΣΥ-146155, ΣΧΎ-4708075, ΣΧ2-12650, ΣΥ2-1080593799 Step 3: Use the following formula to work out the correlation coefficient 11 4708075-330 146155 0.9919 11-12650-330 11-1980593799 1461552

the line fits well as the correlation coefficient is 0.9919 near to 1