Question

 

Steps (all statistical analysis to be done in Excel and/or StatCrunch):

Watch the TED talk by Hans Roling titled “The best stats you’ve ever seen”. You will need to include comments on this in your paper. Here is a link: http://www.ted.com/talks/hans_rosling_shows_the_best_stats_you_ve_ever_seen?language=en

Download the Excel data from IvyLearn

Create histograms of each of the variables (one histogram for fertility, one for life expectancy). Use the histograms to identify the shapes of the distribution. StatCrunch will be the easier tool to use for this particular task.

Calculate some descriptive statistics for each of the variables, including but not limited to the mean, median and standard deviation. Organize these numbers nicely in a table.

Using fertility as the predictor variable and life expectancy as the response variable, create a scatter diagram, come up with the least-squares regression line and calculate the linear correlation coefficient as well as the coefficient of determination. Make sure that you understand all interpretations and include them in your paper. Please carefully review the rubric below to see the full list of required interpretations.

Use the regression line to predict life expectancy for the United States given fertility and then compare this to the actual value in the United States.

Name some possible lurking variables that may be at work here.

Explain the difference between correlation and causation and why we cannot say that there is a cause and effect relationship in this situation.

Explain why we cannot use our regression model to predict the life expectancy of one particular individual.

Take a look at the website where this data was pulled from and comment on how the model might have been different if we used the data from 20, 40 or 60 years ago. Navigate to http://gapminder.org and click on “Gapminder World”. Use the x-axis and y-axis dropdown menus to ensure that ‘life expectancy (years)’ is selected on the y-axis and ‘children per woman (total fertility)’ is selected on the x-axis.

Country	2013 Fertility	2013 Life Expectancy
Afghanistan	4.9	56.2
Albania	1.771	75.8
Algeria	2.795	76.3
Angola	5.863	60.4
Antigua and Barbuda	2.089	75.2
Argentina	2.175	76
Armenia	1.74	73.8
Aruba	1.673	75.455
Australia	1.882	81.8
Austria	1.471	80.8
Azerbaijan	1.924	72.3
Bahamas	1.888	72.5
Bahrain	2.075	79
Bangladesh	2.177	69.5
Barbados	1.849	75.6
Belarus	1.494	70.2
Belgium	1.854	80.2
Belize	2.676	70
Benin	4.845	64.9
Bhutan	2.232	69.4
Bolivia	3.221	71.9
Bosnia and Herzegovina	1.283	77.5
Botswana	2.619	65.8
Brazil	1.801	75
Brunei	1.994	78.7
Bulgaria	1.541	74.5
Burkina Faso	5.605	62
Burundi	6.033	59.8
Cambodia	2.861	67.8
Cameroon	4.78	58.7
Canada	1.67	81.5
Cape Verde	2.292	74.2
Chad	6.263	57.1
Channel Islands	1.459	80.324
Chile	1.82	79.1
China	1.668	76.5
Colombia	2.286	75.6
Comoros	4.714	63.7
Congo, Dem. Rep.	5.933	57.5
Congo, Rep.	4.969	61.5
Costa Rica	1.795	79.8
Cote d'Ivoire	4.866	58.9
Croatia	1.501	77.8
Cuba	1.449	78.3
Cyprus	1.461	82.2
Czech Rep.	1.566	78.2
Denmark	1.88	79.9
Djibouti	3.387	63.4
Dominican Rep.	2.484	73.6
Ecuador	2.559	74.8
Egypt	2.77	70.9
El Salvador	2.184	73.9
Equatorial Guinea	4.845	58.8
Eritrea	4.696	62.1
Estonia	1.604	76.6
Ethiopia	4.519	62.6
Fiji	2.588	66.1
Finland	1.853	80.6
France	1.98	81.7
French Guiana	3.058	77.121
French Polynesia	2.058	76.257
Gabon	4.087	59.1
Gambia	5.751	64.3
Georgia	1.817	72.9
Germany	1.419	80.7
Ghana	3.857	64.9
Greece	1.529	79.8
Greenland	2.077	71.5
Grenada	2.17	71.5
Guadeloupe	2.08	80.947
Guam	2.405	78.854
Guatemala	3.783	72.3
Guinea	4.915	60.2
Guyana	2.546	64
Haiti	3.148	64.3
Honduras	3.001	72
Hong Kong, China	1.135	83.378
Hungary	1.411	75.8
Iceland	2.083	82.8
India	2.479	66.2
Indonesia	2.338	70.5
Iran	1.92	78.3
Iraq	4.026	71.3
Ireland	1.997	80.4
Israel	2.898	82.2
Italy	1.487	82.1
Jamaica	2.26	75.5
Japan	1.419	83.3
Jordan	3.244	78.1
Kazakhstan	2.455	67.8
Kenya	4.382	65.2
Kiribati	2.952	62
Korea, Dem. Rep.	1.988	71.2
Korea, Rep.	1.321	80.5
Kuwait	2.6	80.3
Kyrgyzstan	3.075	68.6
Laos	3.02	65.8
Latvia	1.607	75.3
Lebanon	1.495	78.3
Liberia	4.792	63.1
Libya	2.356	75.6
Lithuania	1.519	75
Luxembourg	1.671	81.1
Macao, China	1.083	80.4
Macedonia, FYR	1.431	76.6
Madagascar	4.468	64.3
Malawi	5.389	57.3
Malaysia	1.964	74.7
Maldives	2.256	79.3
Mali	6.847	57.2
Malta	1.356	82.1
Martinique	1.827	81.41
Mauritania	4.67	65.1
Mauritius	1.501	73.3
Mayotte	3.802	79.19
Mexico	2.185	75.5
Micronesia, Fed. Sts.	3.294	66.8
Moldova	1.456	71.9
Mongolia	2.436	64.7
Montenegro	1.666	75.6
Morocco	2.735	74.3
Mozambique	5.188	56.2
Myanmar	1.938	67.1
Namibia	3.051	60.6
Nepal	2.3	70.6
Netherlands	1.774	80.6
Netherlands Antilles	1.89	76.894
New Caledonia	2.127	76.306
New Zealand	2.052	80.6
Nicaragua	2.498	76.4
Niger	7.561	61.6
Nigeria	5.976	60.1
Norway	1.931	81.4
Oman	2.853	75.5
Pakistan	3.185	65.7
Panama	2.466	77.8
Papua New Guinea	3.781	59.8
Paraguay	2.864	73.7
Peru	2.417	77.1
Philippines	3.043	70
Poland	1.417	76.9
Portugal	1.315	79.8
Puerto Rico	1.636	78.864
Qatar	2.019	81.8
Reunion	2.232	79.646
Romania	1.417	76
Russia	1.595	71.3
Rwanda	4.508	65.3
Saint Lucia	1.912	74.5
Saint Vincent and the Grenadines	1.997	72.7
Samoa	4.147	71.8
Sao Tome and Principe	4.075	68.4
Saudi Arabia	2.644	77.9
Senegal	4.934	65.7
Serbia	1.365	77.7
Seychelles	2.18	73.3
Sierra Leone	4.705	57.7
Singapore	1.282	81.9
Slovak Republic	1.396	76.2
Slovenia	1.509	80
Solomon Islands	4.031	63.7
Somalia	6.563	57.7
South Africa	2.387	60.4
South Sudan	4.92	57.2
Spain	1.505	81.7
Sri Lanka	2.339	76.1
Sudan	4.42	68.9
Suriname	2.268	70.1
Sweden	1.928	81.8
Switzerland	1.533	82.7
Syria	2.964	72.4
Taiwan	1.065	79.3
Tajikistan	3.815	70.6
Tanzania	5.214	62.2
Thailand	1.399	74.9
Timor-Leste	5.855	71.4
Togo	4.639	63
Tonga	3.767	70.3
Trinidad and Tobago	1.797	71.2
Tunisia	2.008	77.1
Turkey	2.041	76.3
Turkmenistan	2.326	67.5
Uganda	5.867	59.8
Ukraine	1.47	71.7
United Arab Emirates	1.801	76.4
United Kingdom	1.892	81
United States	1.976	78.9
Uruguay	2.046	76.9
Uzbekistan	2.309	69.7
Vanuatu	3.382	64.6
Venezuela	2.39	75.4
Vietnam	1.743	76.3
Virgin Islands (U.S.)	2.487	80.152
West Bank and Gaza	4.01	74.6
Western Sahara	2.363	67.764
Yemen, Rep.	4.075	67
Zambia	5.687	56.7
Zimbabwe	3.486	56

Answer 1

Histogram of 2013 Fertility shows that the 2013 Fertility data is positively skewed distribution whereas Histogram of 2013 Life Expectancy shows that the 2013 Life Expectancy data is negatively skewed distribution.

From the scatter plot, it is observed that 2013 Life Expectancy (y) is negatively correlated with 2013 Fertility (x).

Pearson correlation of 2013 Fertility and 2013 Life Expectancy = -0.800

Since P-Value = 0.000<0.05, so correlation coefficient of x and y is significant.

Regression Analysis: 2013 Life Expectancy versus 2013 Fertility

The regression equation is
2013 Life Expectancy = 84.2 - 4.31x 2013 Fertility

Table 1
Predictor Coef SE Coef T P
Constant 84.1613 0.7176 117.28 0.000<0.05
2013 Fertility -4.3090 0.2307 -18.68 0.000<0.05

S = 4.51093 R-Sq = 64.0% R-Sq(adj) = 63.9%

Table 2
Analysis of Variance

Source DF SS MS F P
Regression 1 7101.7 7101.7 349.00 0.000
Residual Error 196 3988.3 20.3
Total 197 11090.0

From Table 1 we observed that Intercept (constant) and Slope (regression coefficient) are significantly present since p-values are less than 0.05.

Hence finally we get the regression equation:

2013 Life Expectancy = 84.2 - 4.31x 2013 Fertility

This regression equation is also significant (since from Table 2, we see that p-value <0.05).

coefficient of determination= 64.0% implies this regression eqution explains  64.0% of total variation in 2013 Life Expectancy.

From the above scatter plot with fitted line it is observed that the fitting is good.

Predicted life expectancy for the United States given fertility=84.2 - 4.31x1.976=75.683

The actual value of life expectancy in the United States=78.900

Residual=78.900-75.683=3.217