Chapter 9 #11-13, 17, 19 AND Respond to this question: How can one point in a scatterplot throw off the entire regression equation, r and r-squared?
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Anonymous
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I suppose for one point to throw off the enitre regression, r, and r-squared, the point would have to be a somewhat extreme outlier with an x and/or y value greatly differing from the other or going away from a linear correlation. If one point is an outlier that follows a linear regression, then it would likely make the regression even better.
One point in a scatterplot can throw off a regression equation if that one point does not follow the overall linear pattern which makes the point an outlier. If the point throws off the linear pattern this in result makes the correlation weaker.
One point can throw off the entire regression equation because if it is an outlier/leverage point it will change the slope, and will weaken the correlation because it will pull the line up or down. Another point that can throw off r and r-squared would be an influential point, meaning it fits the regression line and therefore stregnthens the correlation because it follows the regression line even if it looks like an outlier
A point can throw off the regression equation because it would be a leverage point which would either pull the line down or up. It could chage R by being an outlier and pulling R closer to zero. Or it could make R even stronger by followin the existing regression line. The same effects would happen for R2 as for R
A point can throw off the entire regression equation if it is an outlier.The outlier would be called a leverage point and would pull or drag the line. The outlier would have to have a very large residual to do this. The large residual would weaken the correlation making the r and r-squared differ and get closer to 0.
One point in a scatterplot could throw off the entire regression equation, and r-squared if it were an outlier point or leverage point. The point would in effect drag the regression line either upward or downward weakening the correlation.
One point can throw off the entire regression equation if that point does not follow the overall linear pattern that almost all of the other points follolw. The point would have to be an x point far below the regression line
One point will throw off the entire regression equation because it will weaken r and warp the slope of the regression line. Outliers also affect r squared b/c r squared accounts for the variation in the model. If a point affects r, it will affect r squared as well.
For a point to throw off the entire regression, it would have to be a leverage or influential point. These points would be far off in the x-axis, as this would drag the regression line up or down, which as a result would change r and r2. An outlier also has the capability of doing such, but it would have less of an effect on the regression line.
One point can throw off the entire regression equation by being an influential or leverage point. This would mean that it deviates from the linear pattern, thus altering the slope. Correlation and amount of variation accounted for (r and r squared) can be altered by outliers. Outliers that have a large residual will weaken the correlation. If a point appears far away from the majority of the data, but doesn't have a large residual, it is not necessarily considered to be an outlier. This point would strengthen the correlation because it follows the linear regression.
A point that could essentially throw off the entire regression equation, r and r-squared would be the the leverage point. Lets take the example from the board a couple days ago (100,0) where it was an major outlier and leverage point which would bring down the line thus changing the regression equation, r and r-squared.
Points that can throw off an entire regression is a point of high leverage. This point is also said to be highly influential. The reason being is that this single point has the potential to make r and r-squared zero. It all depends on how much of an outlier the point actually is.
One point on a scatter plot can throw off an entire regression because you can have a point of high or low leverage. if its high leverage it will drag the line up. if its low leverage it will pull the line down. this also screws up r and the correlation.
For a a point to change the entire regression, r, and the R squared the point would need to be a infuential point. The point could not be just an outlier cause an outlier does not change the slope of the regression line. but in influential point can turn a slope of a regression line to the negative or positive. the r and r squared will automaticly be changed when any influential point is added and the change in r automaticly changes the r squared.
15 comments:
I suppose for one point to throw off the enitre regression, r, and r-squared, the point would have to be a somewhat extreme outlier with an x and/or y value greatly differing from the other or going away from a linear correlation. If one point is an outlier that follows a linear regression, then it would likely make the regression even better.
One point in a scatterplot can throw off a regression equation if that one point does not follow the overall linear pattern which makes the point an outlier. If the point throws off the linear pattern this in result makes the correlation weaker.
One point can throw off the entire regression equation because if it is an outlier/leverage point it will change the slope, and will weaken the correlation because it will pull the line up or down. Another point that can throw off r and r-squared would be an influential point, meaning it fits the regression line and therefore stregnthens the correlation because it follows the regression line even if it looks like an outlier
A point can throw off the regression equation because it would be a leverage point which would either pull the line down or up. It could chage R by being an outlier and pulling R closer to zero. Or it could make R even stronger by followin the existing regression line. The same effects would happen for R2 as for R
A point can throw off the entire regression equation if it is an outlier.The outlier would be called a leverage point and would pull or drag the line. The outlier would have to have a very large residual to do this. The large residual would weaken the correlation making the r and r-squared differ and get closer to 0.
One point in a scatterplot could throw off the entire regression equation, and r-squared if it were an outlier point or leverage point. The point would in effect drag the regression line either upward or downward weakening the correlation.
One point can throw off the entire regression equation if that point does not follow the overall linear pattern that almost all of the other points follolw. The point would have to be an x point far below the regression line
One point will throw off the entire regression equation because it will weaken r and warp the slope of the regression line. Outliers also affect r squared b/c r squared accounts for the variation in the model. If a point affects r, it will affect r squared as well.
For a point to throw off the entire regression, it would have to be a leverage or influential point. These points would be far off in the x-axis, as this would drag the regression line up or down, which as a result would change r and r2. An outlier also has the capability of doing such, but it would have less of an effect on the regression line.
One point can throw off the entire regression equation by being an influential or leverage point. This would mean that it deviates from the linear pattern, thus altering the slope. Correlation and amount of variation accounted for (r and r squared) can be altered by outliers. Outliers that have a large residual will weaken the correlation. If a point appears far away from the majority of the data, but doesn't have a large residual, it is not necessarily considered to be an outlier. This point would strengthen the correlation because it follows the linear regression.
A point that could essentially throw off the entire regression equation, r and r-squared would be the the leverage point. Lets take the example from the board a couple days ago (100,0) where it was an major outlier and leverage point which would bring down the line thus changing the regression equation, r and r-squared.
Points that can throw off an entire regression is a point of high leverage. This point is also said to be highly influential. The reason being is that this single point has the potential to make r and r-squared zero. It all depends on how much of an outlier the point actually is.
One point on a scatter plot can throw off an entire regression because you can have a point of high or low leverage. if its high leverage it will drag the line up. if its low leverage it will pull the line down. this also screws up r and the correlation.
For a a point to change the entire regression, r, and the R squared the point would need to be a infuential point. The point could not be just an outlier cause an outlier does not change the slope of the regression line. but in influential point can turn a slope of a regression line to the negative or positive. the r and r squared will automaticly be changed when any influential point is added and the change in r automaticly changes the r squared.
Influential Points are leverage points that are using thier leverage. They are usually outliers in x and ca change the entire slope of a line.
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