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

Solutions

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 1 year ago

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