Chapter 9, Problem 3E

(a)

To determine

To explain why fitting a linear model to these data might be misleading.

Explanation of Solution

The United Nations Development Programme uses the Human development Index (HDI) in an attempt to summarize one number the progress in health, education and economics of the country. The gross domestic product per capita (GDPPC) is often used to summarize the overall economic strength of the country. Thus, they want to study that if the HDI is related to GDPPC or not. The scatterplot of HDI versus GDPPC is given in the question. Now, by looking at the scatterplot we can say that the relationship between the HDI and GDPPC is not straight as the points are forming an unusual pattern in the scatterplot. Thus, we can say that fitting a linear model to these data might be misleading.

(b)

To determine

To explain what do you think a scatterplot of residuals versus predicted HDI will look like if you fit a linear model to the data.

Answer to Problem 3E

It will be curved downward.

Explanation of Solution

The United Nations Development Programme uses the Human development Index in an attempt to summarize one number the progress in health, education and economics of the country. The gross domestic product per capita is often used to summarize the overall economic strength of the country. Thus, they want to study that if the HDI is related to GDPPC or not. The scatterplot of HDI versus GDPPC is given in the question. Now, by looking at the scatterplot we can say that if we fit a linear model to the data then, the pattern will be curved downward compared to the pattern in the scatterplot.

(c)

To determine

To explain will setting this point aside improve the model sustainability or not.

Answer to Problem 3E

No, it will not improve.

Explanation of Solution

The United Nations Development Programme uses the Human development Index in an attempt to summarize one number the progress in health, education and economics of the country. The gross domestic product per capita is often used to summarize the overall economic strength of the country. Thus, they want to study that if the HDI is related to GDPPC or not. The scatterplot of HDI versus GDPPC is given in the question. Now, by looking at the scatterplot we can say that if we remove an outlier in the scatterplot with GDPPC of around $\$70000$ , then it will not improve the model sustainability as it is only one outlier and the sustainability does not depend on one outlier.