Question

To assess the relationship between number of absences and grades, an instructor collects data from the ten students in a class and runs a simple regression. She finds a perfect negative relationship: as the number of absences goes up, grades go down. But then, the instructor remembers that there is an 11th person in the class: someone who never came to class but still managed somehow to get a perfect grade in the course. Conceptually (not mathematically) describe what will happen to the slope and correlation coefficient.

Answer 1

The scatter plot of the data would look somewhat like

Changes in the slope of the regression line:

1. When there are the first 10 data points in the dat set, the relationship is perfectly negative.
2. That means the slope is -1.
3. Now when the 11^th point is added to the data, it is clear that this point is not along the same line as the other points follow.
4. Hence, this would decrease the absolute value of the slope of the line when all the 11 points are considered.
5. Therfore, the new slope will still be negative, but would be greater than -1. The slope will be somewhere in between -1 and 0 excluded.

Changes in the value of the correlation coefficient:

1. It is given that for the first 10 data points, the relation is perfectly negative.
2. Hence the correlation coefficient would be -.
3. Now, an 11^th point is added to the data.
4. This point is not along the trend followed by the other data points.
5. Hence, it will weaken the amount of correlation between the variables.
6. Thus the new correlation cofficient will reduce in magnitude and it would be somewhere in between -1 and 0, -1 and 0 excluded.

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