Question

In: Statistics and Probability

The following dataset contains a random sample of countries. Two variables are included: GDP per capita...

The following dataset contains a random sample of countries. Two variables are included: GDP per capita and infant mortality rate per 1,000 live births. Determine the equation of the best fit line and calculate the r-squared. Interpret all findings.

If you do not show your work for obtaining each portion of the regression equation and r-squared, you will lose extensive points on this exercise.

Country	GDP per Capita (USD)	Infant Mortality Rate
Malaysia	9766.166	6
Slovak Republic	15962.57	5.8
Central African Republic	306.7788	91.5
Cabo Verde	3131.131	20.7
Denmark	52002.15	2.9
Barbados	15660.68	12
Uganda	675.5735	37.7
Maldives	7681.076	7.4
Kiribati	1291.88	43.6
Palau	13498.66	14.2

Expert Solution

Solution:

Let independent variable X = GDP per Capita (USD)

Dependent variable Y = Infant Mortality Rate

Required formulas are given as below:

Correlation coefficient = r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

Slope b = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

Intercept a = Ybar – b*Xbar

The calculation table is given as below:

No.	x	Y	X^2	Y^2	XY
1	9766	6	95377998.34	36.00	58597.00
2	15963	5.8	254803641.00	33.64	92582.91
3	306.8	91.5	94113.23	8372.25	28070.26
4	3131	20.7	9803981.34	428.49	64814.41
5	52002	2.9	2704223604.62	8.41	150806.24
6	15661	12	245256898.06	144.00	187928.16
7	675.6	37.7	456399.55	1421.29	25469.12
8	7681	7.4	58998928.52	54.76	56839.96
9	1292	43.6	1668953.93	1900.96	56325.97
10	13499	14.2	182213821.80	201.64	191680.97
Total	119976.7	241.8	3552898340.40	12601.44	913114.99

n = 10

∑X = 119976.7

∑Y = 241.8

∑X^2 = 3552898340.40

∑Y^2 = 12601.44

∑XY = 913114.99

Xbar = ∑X / n = 119976.7 / 10 = 11997.67

Ybar = ∑Y / n = 241.8 / 10 = 24.18

r = [n∑xy - ∑x∑y]/sqrt[(n∑x^2 – (∑x)^2)*(n∑y^2 – (∑y)^2)]

r = [10*913114.99 - 119976.7*241.8]/sqrt[(10*3552898340.40 – (119976.7)^2)*(10*12601.44 – (241.8)^2)]

r = -19879216 /sqrt[(10*3552898340.40 – (119976.7)^2)*(10*12601.44 – (241.8)^2)]

r = -19879216 / 37783360

r = -0.52614

Slope b = (∑XY – n*Xbar*Ybar)/(∑X^2 – n*Xbar^2)

Slope b = (913114.99– 10*11997.67*24.18)/( 3552898340.40 – 10*11997.67^2)

Slope b = -0.00094

Intercept a = Ybar – b*Xbar

Intercept a = 24.18 – (-0.00094)* 11997.67

Intercept a = 35.46502

Regression equation is given as below:

Y = a + b*X

Y = 35.46502 - 0.00094*X

Coefficient of determination = r^2 = r*r = -0.52614^2 = 0.276823 = 27.68%

orchestra answered 2 years ago

A study modeled the GDP per capita of 24 countries using the variables Regulation Index, an...

A study modeled the GDP per capita of 24 countries using the variables Regulation Index, an index of Ethnolinguistic Diversity, International Trade as a share of GDP, Primary Education rate in %, and 1988 GDP/Capita. Parts of the regression output are shown below. Dependent variable is: GDP/Capita s = 2102 Source Sum of Squares df Mean Square Fratio Regression 2,740,849,111 5 548,169,822 124 Residual 79,502,035 18 4,416,780 Variable Coefficent SE Coeff T-ratio Intercept 10,744.5 9425 1.14 Regulation Index -1334.98 615.2...

The table below shows two countries with their respective GDP per capita at PPP, life expectancy,...

The table below shows two countries with their respective GDP per capita at PPP, life expectancy, adult literacy, and Gross enrolment rates in 2017, as well as the UNDP’s minimum and maximum rates. Country GDP per capita PPP in $ Life Expectancy at birth in years Adult literacy rate in % Gross enrolment rate in % Greece Ghana 28,517 4,200 79.1 63.5 97.1 45.5 98.5 75.5 Minimum Maximum 100 40,000 25 85 0 100 0 100 Explain the UNDP Human...

Consider the following data on real GDP per capita in: Year Per Capita Real GDP 1950...

Consider the following data on real GDP per capita in: Year Per Capita Real GDP 1950 14 339 1960 17 351 1970 23 790 1980 30 732 1990 35 868 2000 43 288 2010 46 406 2011 47 554 2012 47 741 2013 48 066 2014 48 780 a) Calculate the percentage growth rates in real GDP per capita in each of the years 2011 through 2014, from the previous year. b) Now, instead of calculating the annual percentage growth...

Please do it by type not pics. 1.The following table contains per capita real GDP for...

Please do it by type not pics. 1.The following table contains per capita real GDP for 11 countries for the years 1950 and 2014. Compare a selected group of country’s GDP as compared to Argentina. Are there any “unusual” observations you can make about the data? Based on your knowledge of the countries, discuss some possible explanations of why some countries do better than others. Next, calculate the average real GDP growth rate for each country. I would recommend copying...

All countries do not converge to the same level of per capita GDP as the United...

All countries do not converge to the same level of per capita GDP as the United States, Germany, and Japan. Discuss the reasons behind this.

This dataset contains two variables: fertilizer type (1, 2, or 3) and crop yield per square...

This dataset contains two variables: fertilizer type (1, 2, or 3) and crop yield per square foot. Using ANOVA, test the null hypothesis that the three fertilizers are equally effective. Hint: Notice that the data are arranged in what's called a "long" format (one long column of data). To you ANOVA, you first need to rearrange the data into three columns. 1. What is the value of the F-statistic? Answer 2. What is the p-value that the three means are...

The following dataset contains a random sample of lifetime of 120 BMW Xenon headlight bulbs. The...

The following dataset contains a random sample of lifetime of 120 BMW Xenon headlight bulbs. The manufacturer of these bulbs wants to know whether it can claim that the bulbs last more than 1000 hours. Use a=0.01 93 1053.74 94 1032.37 95 1003.42 96 908.74 97 1037.92 98 1096.83 99 1169.07 100 842.85 101 1038.22 102 973.30 103 996.08 104 984.70 105 989.44 106 1023.07 107 1047.95 108 1073.63 109 1021.51 110 977.27 111 928.44 112 910.28 113 990.68 114...

Using GDP per capita to compare living standards in different countries a. does not account for...

Using GDP per capita to compare living standards in different countries a. does not account for big differences in the distribution of income in these countries. b. overlooks the fact that China has a huge population and Norway is very small. c. is such a poor measure that economists do not use it anymore. d. shows you that America has the highest standard of living in the world. Owning stock in a company a. represents part ownership in the company....

It is found that the real GDP per capita of developing countries grows faster than developed...

It is found that the real GDP per capita of developing countries grows faster than developed countries at the same period. Explain this phenomenon in the light of diminishing returns to capital.

Find a recent list of countries with per capita GDP. Look at the list. Get an idea...

Find a recent list of countries with per capita GDP. Look at the list. Get an idea of which are the rich countries, and which are the poor. What patterns do you see with the rich and poor countries? Which source did you use? How does it vary from other lists? Write one page (single-spaced) summary of what trends you see on this list. Make sure you reference your source.