Question

QUESTION TWO The following outputs show the results of a study conducted on life expectancy of some sampled people across the globe. Three important variables were of interest. They were adult illiteracy, quality of life and family size. Outputs: Table 2. ANOVA Model df Sig. Sum of Squares 34427.688 3870.862 38298.550 Mean F Square 11475.896 521.785 21.994 Regression Residual Total w 0.000 176 179 Table 3. Coefficients Model Sig. (Constant) Adult Illiteracy Quality of Life Rel. Family Size Unstandardized Coefficients B Std. Error 78.633 3.145 -0.374 0.023 0.555 0.365 - 1.783 0.306 Standardized Coefficients Beta 25.002 -.688 -16.260 .062 1.519 -250 -5.827 0.000 0.000 0.131 0.000 a) Write a regression model for this study. State any two assumptions underlying this model. b) What is the dependent variable? c) Perform statistical tests to explain the significance of the predictor variables in the regression model (use the results in Tables 2 and 3).

Answer 1

a) Life expectancy = 78.663 - 0.374*Adult Literacy + 0.555*Quality of Life - 1.783*Rel. Family size

Assumptions:

1. There is no correlation between independent variables

2. Residuals or error terms are normally distributed

b) Dependent variable: Life expectancy of an individual

c) Significance of all predictors

H₀: β₁ = β₂ = β₃ = 0, The model is not a good fit to predict life expectancy

H₁: At least one of β_i ≠ 0, The model is a good fit to predict life expectancy

p-value (Sig. ANOVA) = 0.000

Level of significance = 0.05

Since p-value is less than 0.05, we reject the null hypothesis and conclude that aleast one of β_i ≠ 0.

So, the model is a good fit to predict life expectancy.

Significance of Adult Literacy

H₀: β₁ = 0, Adult literacy is not a significant predictor of life expectancy

H₁: β₁ ≠ 0, Adult literacy is a significant predictor of life expectancy

p-value (Sig. of adult literacy) = 0.000

Level of significance = 0.01

Since p-value is less than 0.05, we reject the null hypothesis and conclude that β₁ ≠ 0.

So, adult literacy is a significant predictor of life expectancy.

Significance of Quality of Life

H₀: β₂ = 0, Quality of life is not a significant predictor of life expectancy

H₁: β₂ ≠ 0, Quality of life is a significant predictor of life expectancy

p-value (Sig. of Quality of life) = 0.131

Level of significance = 0.05

Since p-value is more than 0.05, we do not reject the null hypothesis and conclude that β₂ = 0.

So, quality of life is a significant predictor of life expectancy.

Significance of Relative family size

H₀: β₃ = 0, Relative family size is not a significant predictor of life expectancy

H₁: β₃ ≠ 0, Relative family size is a significant predictor of life expectancy

p-value (Sig. of adult literacy) = 0.000

Level of significance = 0.05

Since p-value is less than 0.05, we reject the null hypothesis and conclude that β₃ ≠ 0.

So, relative family size is a significant predictor of life expectancy.