Question

10. Birth Rate and Life Expectancy

Use the dataset AllCountries to examine the correlation between birth rate and life expectancy across countries of the world.

Country	BirthRate	LifeExpectancy
Afghanistan	34.1	60.9
Albania	12.9	77.5
Algeria	24.3	71.0
American Samoa
Andorra
Angola	44.1	51.9
Antigua and Barbuda	16.5	75.8
Argentina	16.8	76.2
Armenia	13.7	74.5
Aruba	10.3	75.3
Australia	13.2	82.2
Austria	9.4	80.9
Azerbaijan	18.3	70.7
Bahamas, The	15.3	75.1
Bahrain	15.2	76.7
Bangladesh	20.0	70.7
Barbados	12.7	75.3
Belarus	12.5	72.5
Belgium	11.2	80.4
Belize	23.4	73.9
Benin	36.4	59.3
Bermuda	10.4	80.6
Bhutan	19.6	68.3
Bolivia	25.7	67.2
Bosnia and Herzegovina	9.0	76.3
Botswana	23.6	47.4
Brazil	14.9	73.9
Brunei Darussalam	15.5	78.6
Bulgaria	9.2	74.5
Burkina Faso	40.9	56.3
Burundi	44.7	54.1
Cabo Verde	20.1	74.9
Cambodia	25.7	71.7
Cameroon	37.3	55.0
Canada	10.9	81.4
Cayman Islands	12.5
Central African Republic	34.2	50.1
Chad	45.9	51.2
Channel Islands	9.5	80.3
Chile	13.9	79.8
China	12.1	75.4
Colombia	18.8	74.0
Comoros	35.2	60.9
Congo, Dem. Rep.	42.7	49.9
Congo, Rep.	37.6	58.8
Costa Rica	15.1	79.9
Cote d'Ivoire	36.6	50.8
Croatia	9.4	77.1
Cuba	9.5	79.2
Curacao	12.7
Cyprus	11.5	79.8
Czech Republic	10.2	78.3
Denmark	10.0	80.3
Djibouti	27.5	61.8
Dominica
Dominican Republic	20.8	73.5
Ecuador	20.8	76.5
Egypt, Arab Rep.	23.2	71.1
El Salvador	20.1	72.3
Equatorial Guinea	35.4	53.1
Eritrea	36.7	62.8
Estonia	10.3	76.4
Ethiopia	33.0	63.6
Faeroe Islands		81.3
Fiji	20.4	69.9
Finland	10.7	80.8
France	12.3	82.0
French Polynesia	16.4	76.3
Gabon	31.9	63.4
Gambia, The	42.7	58.8
Georgia	13.3	74.1
Germany	8.5	81.0
Ghana	30.9	61.1
Greece	8.5	80.6
Greenland	14.5
Grenada	19.3	72.7
Guam	17.4	78.9
Guatemala	31.0	72.0
Guinea	36.9	56.1
Guinea-Bissau	37.5	54.3
Guyana	20.3	66.2
Haiti	25.6	63.1
Honduras	25.8	73.8
Hong Kong SAR, China	7.9	83.8
Hungary	9.2	75.3
Iceland	13.4	83.1
India	20.4	66.5
Indonesia	18.8	70.8
Iran, Islamic Rep.	18.8	74.1
Iraq	31.1	69.5
Ireland	15.0	81.0
Isle of Man
Israel	21.3	82.1
Italy	8.5	82.3
Jamaica	13.5	73.5
Japan	8.2	83.3
Jordan	27.0	73.9
Kazakhstan	22.7	70.5
Kenya	34.9	61.7
Kiribati	23.3	68.8
Korea, Dem. Rep.	14.4	69.8
Korea, Rep.	8.6	81.5
Kosovo	17.7	70.8
Kuwait	20.6	74.5
Kyrgyz Republic	27.2	70.2
Lao PDR	26.8	68.2
Latvia	10.2	74.0
Lebanon	13.4	80.1
Lesotho	27.5	49.3
Liberia	35.5	60.5
Libya	20.7	75.4
Liechtenstein	9.2	82.4
Lithuania	10.1	74.2
Luxembourg	11.3	81.8
Macao SAR, China	10.2	80.3
Macedonia, FYR	10.7	75.2
Madagascar	34.7	64.7
Malawi	39.8	55.2
Malaysia	17.7	75.0
Maldives	22.0	77.9
Mali	47.1	55.0
Malta	9.5	80.7
Marshall Islands
Mauritania	34.1	61.5
Mauritius	10.9	74.5
Mexico	18.4	77.4
Micronesia, Fed. Sts.	23.5	69.0
Moldova	12.1	68.8
Monaco
Mongolia	22.7	67.5
Montenegro	11.6	74.8
Morocco	22.7	70.9
Mozambique	38.9	50.2
Myanmar	17.2	65.1
Namibia	26.0	64.3
Nepal	21.0	68.4
Netherlands	10.2	81.1
New Caledonia	17.0	77.1
New Zealand	13.1	81.4
Nicaragua	22.7	74.8
Niger	49.7	58.4
Nigeria	41.2	52.5
Northern Mariana Islands
Norway	11.6	81.5
Oman	20.9	76.9
Pacific island small states	24.7	69.9
Pakistan	25.2	66.6
Palau	13.1
Panama	19.4	77.6
Papua New Guinea	28.9	62.4
Paraguay	23.7	72.3
Peru	19.7	74.8
Philippines	24.4	68.7
Poland	9.6	76.8
Portugal	7.9	80.4
Puerto Rico	10.8	78.7
Qatar	11.0	78.6
Romania	8.8	74.5
Russian Federation	13.2	71.1
Rwanda	35.2	64.0
Samoa	26.2	73.3
San Marino
Sao Tome and Principe	33.9	66.3
Saudi Arabia	19.4	75.7
Senegal	37.7	63.4
Serbia	9.2	75.1
Seychelles	18.6	74.2
Sierra Leone	36.6	45.6
Singapore	9.3	82.3
Sint Maarten (Dutch part)
Slovak Republic	10.1	76.3
Slovenia	10.2	80.3
Solomon Islands	30.8	67.7
Somalia	43.8	55.0
South Africa	20.9	56.7
South Sudan	36.1	55.2
Spain	9.1	82.4
Sri Lanka	17.9	74.2
St. Kitts and Nevis
St. Lucia	15.4	74.8
St. Martin (French part)	16.0	79.2
St. Vincent and the Grenadines	16.3	72.5
Sudan	33.5	62.0
Suriname	17.7	71.0
Swaziland	29.9	48.9
Sweden	11.8	81.7
Switzerland	10.2	82.7
Syrian Arab Republic	24.0	74.7
Tajikistan	33.0	67.4
Tanzania	39.2	61.5
Thailand	10.2	74.4
Timor-Leste	35.8	67.5
Togo	36.4	56.5
Tonga	25.5	72.6
Trinidad and Tobago	14.5	69.9
Tunisia	19.8	73.6
Turkey	16.8	75.2
Turkmenistan	21.3	65.5
Turks and Caicos Islands
Tuvalu
Uganda	43.2	59.2
Ukraine	11.1	71.2
United Arab Emirates	14.5	77.1
United Kingdom	12.2	81.0
United States	12.5	78.8
Uruguay	14.5	77.1
Uzbekistan	22.5	68.2
Vanuatu	26.6	71.7
Venezuela, RB	19.8	74.6
Vietnam	15.5	75.8
Virgin Islands (U.S.)	10.7	79.6
West Bank and Gaza	30.4	73.2
Yemen, Rep.	31.1	63.1
Zambia	42.8	58.1
Zimbabwe	31.3	59.8

(a) Plot the data. Do birth rate and life expectancy appear to be linearly associated?
Upload a screenshot of your scatterplot.

(b) From this dataset, can we conclude that the population correlation between birth rate and life expectancy is different from zero?

(c) Explain why inference is not necessary to answer part (b).

(d) For every percent increase in birth rate, how much does the predicted life expectancy of a country change?

(e) From this dataset, can we conclude that lowering the birth rate of a country will increase its life expectancy? Why or why not?

Answer 1

a)

b)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	4278.2	14016.2	22171.98219	16273.9	-14388.62
mean	21.28	69.73	SSxx	SSyy	SSxy

sample size ,   n =   201          
here, x̅ = Σx / n=   21.28   ,     ȳ = Σy/n =   69.73  
                  
SSxx =    Σ(x-x̅)² =    22171.9822          
SSxy=   Σ(x-x̅)(y-ȳ) =   -14388.6          
                  
estimated slope , ß1 = SSxy/SSxx =   -14388.6   /   22171.982   =   -0.6490
                  
intercept,   ß0 = y̅-ß1* x̄ =   83.5451          
                  
so, regression line is   Ŷ =   83.5451   +   -0.6490   *x
                  
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    6936.348          
                  
std error ,Se =    √(SSE/(n-2)) =    5.904          
                  
correlation coefficient ,    r = Sxy/√(Sx.Sy) =   -0.7575          

c)

Inference is not necessary as we can see that r is higher and plot clearly see the relatioship

d)

estimated slope , ß1 = SSxy/SSxx =   -14388.6   /   22171.982   =   -0.6490

For every percent increase in birth rate, the predicted life expectancy of a country decrease by 0.6490

e)

Yes we can conclude that lowering the birth rate of a country will increase its life expectancy as slope is negative and relationship is strong negative

Please revert back in case of any doubt.

Please upvote. Thanks in advance.