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By adding the point in bold, what will be the effect on the slope of the regression line?

1) The slope of the regression line will increase
2) The slope of the regression line will decrease
3) The slope of the regression line will remain the same
4) Cannot be determined without additional information

1 Answer

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Final answer:

The effect on the slope of the regression line from adding a new data point cannot be determined without knowing the location of this point in relation to the current data. The new point could increase or decrease the slope, or leave it unchanged.

Step-by-step explanation:

The effect of adding a point in bold on the slope of the regression line cannot be determined without additional information. The slope represents how the dependent variable changes for every one unit increase in the independent variable, and adding a new data point can either increase, decrease, or have no effect on the slope depending on where the point is added in relation to the current data points on the graph.

If the new point is above the current regression line and to the right of the other data points, it would typically increase the slope, causing the line to rotate counter-clockwise around the y-intercept. Conversely, if the point is below the regression line and to the left, it would decrease the slope, causing the line to rotate clockwise. If the new point lies exactly on the current regression line, then the slope would remain the same.

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