2. the heights and weights of a random sample of 22 individuals are shown in the scatterplot. the least…

2. the heights and weights of a random sample of 22 individuals are shown in the scatterplot. the least squares regression line describing the relationship between x = height (in inches) and y = weight (in pounds) is given along with the r² value and the residual plot. is a linear model appropriate for these data? give several reasons to justify your answer.

2. the heights and weights of a random sample of 22 individuals are shown in the scatterplot. the least squares regression line describing the relationship between x = height (in inches) and y = weight (in pounds) is given along with the r² value and the residual plot. is a linear model appropriate for these data? give several reasons to justify your answer.

Answer

Brief Explanations:

  1. Scatter - plot: The points in the scatter - plot seem to roughly follow a linear pattern, indicating a possible linear relationship between height and weight.
  2. Residual plot: The residual plot shows points randomly scattered around the horizontal axis. This randomness suggests that the errors are independent and there is no obvious non - linear pattern in the residuals.
  3. (r^{2}) value: The (r^{2}=0.795) indicates that about 79.5% of the variation in weight can be explained by the linear relationship with height. A relatively high (r^{2}) value further supports the use of a linear model.

Answer:

Yes, a linear model is appropriate for these data. Reasons include: the scatter - plot shows a roughly linear pattern, the residual plot has randomly scattered points, and the relatively high (r^{2}) value of 0.795.