Answer:
Step-by-step explanation:
Hello!
The variables of interest are:
X₁: Percentage of GDP spent on health expenditure of a country.
X₂: Percentage of women that received prenatal care in a country.
Using the data you have to calculate the coefficient of correlation between these two variables and the coefficient of determination.
There is a mathematical relationship between these two coefficients if you calculate the coefficient of correlation between two variables and the square it, you obtain the coefficient of determination.
[tex]r= \frac{SumX_1X_2-\frac{(SumX_1)(SumX2)}{n} }{\sqrt{[SumX_1^2-\frac{(SumX_1)^2}{n} ][SumX_2^2-\frac{(SumX_2)^2}{n} ]} }[/tex]
n=15; ∑X₁=91.90; ∑X₁²=619.77; ∑X₂=1198.70; ∑X₂²=101110.53; ∑X₁X₂= 7438.24
[tex]r= \frac{7438.24-\frac{91.90*1198.70)}{15} }{\sqrt{[619.77-\frac{(91.90)^2}{15} ][101110.53-\frac{(1198.70)^2}{15} ]} }= 0.17[/tex]
The coefficient of correlation shows the degree of association between two variables X₁ and X₂. Its range is from -1 to 1
If r = 0 then there is no linear correlation between X₁ and X₂ Graphically, the slope is cero
If r < 0 then there is a negative association between X₁ and X₂ (i.e. when one variable increases the other one decreases) In a graphic, the slope of the line is negative.
If r > 0 then there is a positive association between X₁ and X₂ (i.e. Both variables increase and decrease together)
The closer to 1 or -1 the coefficient is, the stronger the association between variables.
The calculated coefficient 0.17 is close to zero, this means that presumably there is no association between the percentage of GDP spent on health insurance and the percentage of prenatal care received by women in the countries.
R²= r²= 0.17²= 0.0289⇒ 2.89%
The coefficient of determination shows the percentage of the variability of the dependent variable is explained by the independent variable under the estimated regression model.
Its range is 0 to 1 or, in percentage, 0 to 100%
If the value of R² is close to zero, this means that there is no functional relationship between the dependent and independent variables, i.e. there is no linear regression between the two variables.
If the value of R² is close to 100%, then there is a strong linear regression between these two variables.
If we consider X₁ as the dependent variable and X₂ as the independent variable.
R²= 2.89% indicates that, in the context of the linear regression, almost 3% of the variability of the GDP percentage spent on health expenditures ins explained by the percentage of women that receive prenatal care. There is no linear regression between these two variables.
I hope this helps!
