The data set infmort from the faraway package contains information on the mortal

Question

The data set infmort from the faraway package contains information on the mortality of infants for 105 nations. The variable mortality gives the number of deaths per 1000 live births, while income is the per capita income in US dollars and region indicates the geographic area of the nation. Consider the model E(log(mortality)|income, region) = 0 + 1 log(income) + 2region + 12region log(income).

(a) State the null and alternative hypotheses for the overall F-test for this model. Perform the test and summarize results. (b) Explain the practical meaning of the hypothesis H0 : 12 = 2 = 0 in the context of the above model. (c) Perform a test for the hypothesis in part b) and summarize your results.

Explanation / Answer

Please see the R snippet as shoen below

install.packages("faraway")

library("faraway")
data("infmort")
inf
## regression

fit <- lm(log(mortality) ~ region + log(income) + log(income)*region,data=infmort)
summary(fit)

The results are

summary(fit)

Call:
lm(formula = log(mortality) ~ region + log(income) + log(income) *
region, data = infmort)

Residuals:
Min 1Q Median 3Q Max
-1.46809 -0.26530 -0.02148 0.27478 3.14219

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 4.9385 0.6362 7.763 1.06e-11 ***
regionEurope 2.0882 1.8422 1.134 0.2599
regionAsia 1.2634 0.8561 1.476 0.1434
regionAmericas 1.5661 1.1856 1.321 0.1898
log(income) -0.0112 0.1235 -0.091 0.9280
regionEurope:log(income) -0.5205 0.2516 -2.069 0.0413 *
regionAsia:log(income) -0.3798 0.1580 -2.404 0.0182 *
regionAmericas:log(income) -0.3978 0.1979 -2.010 0.0473 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.5971 on 93 degrees of freedom
(4 observations deleted due to missingness)
Multiple R-squared: 0.6464,   Adjusted R-squared: 0.6198
F-statistic: 24.29 on 7 and 93 DF, p-value: < 2.2e-16

a)The hypothesis is

Ho : The model is not statisitcally significant

H1 : The model is statistically significant

So we see that the p value is p-value: < 2.2e-16 , which is less than 0.05 , hence model as a whole is statistically significant

we see that all the b12 p-values , who are less than 0.05 are statisitcally signficant and the p values that are more than 0.05 are not considered significant.

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