Chapter 3, Problem 12PT

(a)

To determine

To identify: the unusual point and explain.

Answer to Problem 12PT

Point A can be described as an outlier/unusual point since it falls outside of the overall pattern.

Explanation of Solution

Given:

  

From the scatter plot, we can see that Point A (value corresponding to isotope value -19.3 and silicon value of 345) is extreme in the X direction as well as in Y direction with no other point near it. So it pulls the regression line toward itself.

(b) (i)

To determine

To describe: the effect on the correlation.

Answer to Problem 12PT

Correlation will increase.

Explanation of Solution

From part (A), we can see that point A is an outlier.

If point A is removed from the scatter plot, correlation will increase since remaining points are more tightly clustered in a linear pattern.

(b) (ii)

To determine

To describe: the effect on the slope and y intercept of the least-squares line.

Answer to Problem 12PT

The Y-intercept increase when the extreme value is removed from the scatter plot.

Explanation of Solution

Point A (Value corresponding to isotope value -19.3 and silicon value of 345) is extreme in the X direction as well as in Y direction with no other point near it. So it pulls the regression line toward itself.

If we remove the extreme value which corresponds to the higher value of silicon, the slope of regression line would decrease as the regression line move towards X-axis.

Also, the Y-intercept increase when the extreme value is removed from the scatter plot.