Chapter 4.2, Problem 4.44E

(a)

To determine

To find out that the relationship between these two variables most likely a result of causation, confounding or common response and justify.

Answer to Problem 4.44E

Common response.

Explanation of Solution

It is a common response because there is a lurking variable that influences the two variable, which is made apparent by the seemingly two groups in the scatterplot.

(b)

To determine

To write a brief analysis that demonstrates your understanding of the material in this chapter by following the four step statistical problem solving process.

Explanation of Solution

Step 1): Plan: we want to investigate the relationship between two variables.

Step2): Collect data: we will investigate the relationship between two variables by constructing a scatterplot. If the scatterplot does not show strong curvature then, we also determine the least square regression line, residual plot, correlation r , and the square of correlation ${\text{r}}^2$ .

Step 3): Analyze data: the scatterplot plots the data pairs with the x -variables on the horizontal axis and the y -variables on the vertical axis.

The least square regression line is the line that minimizes the vertical squared distance of the points to the line.

The residual plot is the same as the scatterplot with the y -variable replaced by the residuals. A residual is the difference between the y -value and the predicted y -value.

The correlation can be determined by the formula:

  $r=\frac{1}{n-1}{\displaystyle \sum [(\frac{x-\overline{x}}{s_x})(\frac{y-\overline{y}}{s_y})]}$

Step 4): Interpret the result: if the scatterplot does not show strong curvature, then it is appropriate to determine the least squares regression line.

  ${\text{r}}^2$ represents the percentage of the variation of the y -variable explained by the least squares regression line.