A study of nutrition in developing countries collected data from the Egyptian village of Nahya. Researchers recorded the mean weight (in kilograms) for 170 infants in Nahya each month during their first year of life. A hasty user of statistics enters the data into software and computes the least-squares li~thout looking at the scatterplot first. The result is weight= 4.88 + 0.267 (age).

Required:
Use the residual plot to determine if this linear model is appropriate.

In regression, the difference amid the observed-value of the dependent-variable (y) and the predicted-value ([tex]\hat y[/tex]) is known as the residual (e).

[tex]e=y-\hat y[/tex]

A residual plot is a graphical representation of the residuals on the y-axis and the independent variable on the x-axis. If the data-points on the residual plot are randomly spread around the x-axis, a linear regression model is appropriate for the data. And if the residual plots shows a non-random or a U or inverted U pattern, a nonlinear model is more appropriate for the data.

The residual provided shown an inverted U pattern. That is the points are not scattered around he graph.

Thus, the linear model is not appropriate.

MrRoyal MrRoyal · Answer 2 · 2021-10-24T14:57:12+02:00

A residual plot for the nutrition data would display the residuals on the y-axis and the age on the x-axis.

The residual plot is not appropriate for a linear model.

From the residual plot (see attachment), we can see that the points on the residual plot follows a curved pattern.

For a residual plot to be a linear model, the points on the plot must be at random on the horizontal axis of the plot.

This means that, the residual plot is not appropriate for a linear model.