The accompanying scatterplot gives data from a random sample of 27 countries whe

Question

The accompanying scatterplot gives data from a random sample of 27 countries where the response variable is infant mortality (deaths per l,000 live births) and the explanatory variable is the gross domestic product (GDP) per capita (in thousands of dollars). The gross domestic product per capita is a representation of a country's standard of living. 100 60 40 20 10 20 30 50 GDP per capita (a) Describe the relationship between infant mortality and GDP per capita. Is this relationship linear? (b) The regression line is also included in the scatterplot. Will this regression line be a good prediction of infant mortality given GDP per capita? Why or why not? Sometimes we can transform data that don't fit a linear pattern in such a way that they do fit a linear pattern. We calculated the logarithm of all the values of both the infant mortality and GDP per capita and plotted the results in the scatterplot below.

Explanation / Answer

a) In the first graph , the relationship is not linear as the fitted regression line does not follow the points given in the graph

b) As the points do not follow the fitted straight regression line , hence the fitted regression line is not a good fit for estimating the infant mortality . Also please note that the line is in the opposite direction hence the relationship is negative

c) The second graph depicts a linear relationship between the variables on a transformed scale. The points closely follow the fitted regression line and is thus a good fit

d) Yes , as stated above the point and regression line follow each other closely , hence this regression on the transformed variable is a good fit .

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