Chapter 9, Problem 4E

(a)

To determine

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

Explanation of Solution

The number of cell phone users per $1000$ people is positively associated with economic progress in a country. So, they want to study about can the number of cell phone subscribers be used to predict the HDI or not. The scatterplot of HDI against cell phone subscribers is given in the question. Thus, by looking at the scatterplot, we can say that if we fit a linear model to these that then the data eventually levels off and would be better modeled by natural log model. And also the data does not follow the linear pattern. So, this will be misleading.

(b)

To determine

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

Answer to Problem 4E

The scatterplot of residual versus predicted HDI will not like that there would be a good mix of positive and negative residuals at first, but eventually, most if not all would become negative.

Explanation of Solution

The number of cell phone users per $1000$ people is positively associated with economic progress in a country. So, they want to study about can the number of cell phone subscribers be used to predict the HDI or not. The scatterplot of HDI against cell phone subscribers is given in the question. Thus, by looking at the scatterplot, we can say that if we fit a linear model to the data then the linear model may somewhat accurately predict the data initially, but once the data starts leveling off, the linear model would begin predicting values above the actual values, thus making most of the residuals negative. So, the scatterplot of residual versus predicted HDI will not like that there would be a good mix of positive and negative residuals at first, but eventually, most if not all would become negative.