When you generate a 'best fit' line for data as presented in the charts of Exhibit A(for example) please also provide your chi-square, or better yet your R^2 value to give us an idea of how well the trend line represents the aggregated data points and their frequency(weekly I guess). Some of those best fit will have a decent R^2 number, …
When you generate a 'best fit' line for data as presented in the charts of Exhibit A(for example) please also provide your chi-square, or better yet your R^2 value to give us an idea of how well the trend line represents the aggregated data points and their frequency(weekly I guess). Some of those best fit will have a decent R^2 number, but several of them will have a very poor R^2. I ask this not as a skeptic but for those who would attack your data and summary conclusions as unfulfilled by lacking some measure of trust. Thank you.
Even though this is deaths indexed against time (MMWR week), this is not a true regression fit exercise between two independent variables.
1. This is an arrival distribution over time. I am not evaluating how well a particular time series of data fits a linear regression line. That is irrelevant. The arrival could have an R^2 of .18 and be perfectly coherent and informative as an arrival function. Cancer in particular will have a bad fit - but its inference will be the strongest in the signal group.
2. This is the formulation of an inflection point (as change between two underlying functions), not an assessment of the single relationship between two independent variables.
3. There are varying levels of confidence to the weeks contained in the series. They are not all equal in strength. The weeks the CDC tampered with are low confidence and should not count in the R^2, as well - the final weeks are also of weaker confidence. An R^2 would tell me academic fiction and maybe even signal that I did not know what I was doing, to a systems pro who understands points 1 - 4 here.
4. A reverse chi-squared arrival will have a horrid R^2 fit, but tell a very significant story - so the two are not related much.
You will see the 'why' of all this in the next article.
When statisticians see a trend line curve, superimposed on a set of distributed data points, and no R^2 value they are going to wonder what it is. In fact, not only would I insist on a R^2 value for your post-inflection point, but I would insist on the same for the weeks prior to that inflection point. We can then make a qualitative comparison to the 'best fit' of the data. This is true whether there are two independent variables(there aren't, time is not independent), or six. You have broken them down in Exh A nicely. An R^2 for the pre-inflection is always going to be better than the post-inflection. Due in some major part to the grenade(jab of death/vax) that was tossed into the population.
If you don't have those regression analysis done, someone will do them for you(like me), and use it as a weapon to discount your potential conclusion. Frex: "Looking at the data in Exh A, I have calculated an R^2 value for the pre-inflection of 0.712. However, calculations of the R^2 value for the post-inflection points runs from a miserable 0.416 down to a disastrous value of 0.18. The only thing that can be determined from these trend lines is that anything post-inflection may be attributed to herd of elk migrating, or phase of the moon, or the phrenology of the author." (no offense meant).
Perhaps making inferences without supporting statistics is why many skeptics are raked over the coals. I await the next articles and their supporting evidence. Thank you, doc
"Looking at the data in Exh A, I have calculated an R^2 value for the pre-inflection of 0.712. However, calculations of the R^2 value for the post-inflection points runs from a miserable 0.416 down to a disastrous value of 0.18."
A person who contended this would be a complete idiot, and I would never listen to another thing they said. These are 'Variations Against Trend (Baseline)' charts - they have an inherent 'bias to R^2 fit'. Any lower R^2 or departure from fit indicates a SIGNAL, not the lack of one.
I think you are missing this, and the four points I made.
You just used the word Trend in your quotes. The trend line represents the linear interpolation of the data points. This is true no matter what signal you are trying to convey. Point 1 is an excellent example of where a regression is called for. Point 2 is what you are trying to convey, or signal. No problem.
In closing, if you leave the trend line out(post-inflection), you would have no concern about the R^2 value, and the non-statistics among us can make and see their own best fit. Your 'aha!' moment. If/when you are going to put a linear regression trend line(post-inflection) of the data points to prove your signal direction and magnitude, leaving out an R^2 value - even if it is worse than pre-inflection is a mistake. As noted, we expect the regression to get worse. But no matter the delta R^2, from pre and post-inflection, either do or don't for both.
Trend and 'linear fit' are not congruent, despite your insistence that they are. There exists such a thing called Non-Linear optimization (my Major is in this). It uses the Golden Section method to conduct regression/trend analysis.
As you can see below, gravity (no inflection, single function, and indeed a TREND) produces a trend in the motion of a planet, but if you place an R^2 on it the fit is going to be horrible. Does that mean that gravity does not exist!!!!!!!!!!?????
This is what you are saying - that gravity does not exist, because it doesn't fit an R^2 well.
When you generate a 'best fit' line for data as presented in the charts of Exhibit A(for example) please also provide your chi-square, or better yet your R^2 value to give us an idea of how well the trend line represents the aggregated data points and their frequency(weekly I guess). Some of those best fit will have a decent R^2 number, but several of them will have a very poor R^2. I ask this not as a skeptic but for those who would attack your data and summary conclusions as unfulfilled by lacking some measure of trust. Thank you.
Even though this is deaths indexed against time (MMWR week), this is not a true regression fit exercise between two independent variables.
1. This is an arrival distribution over time. I am not evaluating how well a particular time series of data fits a linear regression line. That is irrelevant. The arrival could have an R^2 of .18 and be perfectly coherent and informative as an arrival function. Cancer in particular will have a bad fit - but its inference will be the strongest in the signal group.
2. This is the formulation of an inflection point (as change between two underlying functions), not an assessment of the single relationship between two independent variables.
3. There are varying levels of confidence to the weeks contained in the series. They are not all equal in strength. The weeks the CDC tampered with are low confidence and should not count in the R^2, as well - the final weeks are also of weaker confidence. An R^2 would tell me academic fiction and maybe even signal that I did not know what I was doing, to a systems pro who understands points 1 - 4 here.
4. A reverse chi-squared arrival will have a horrid R^2 fit, but tell a very significant story - so the two are not related much.
You will see the 'why' of all this in the next article.
TES
When statisticians see a trend line curve, superimposed on a set of distributed data points, and no R^2 value they are going to wonder what it is. In fact, not only would I insist on a R^2 value for your post-inflection point, but I would insist on the same for the weeks prior to that inflection point. We can then make a qualitative comparison to the 'best fit' of the data. This is true whether there are two independent variables(there aren't, time is not independent), or six. You have broken them down in Exh A nicely. An R^2 for the pre-inflection is always going to be better than the post-inflection. Due in some major part to the grenade(jab of death/vax) that was tossed into the population.
If you don't have those regression analysis done, someone will do them for you(like me), and use it as a weapon to discount your potential conclusion. Frex: "Looking at the data in Exh A, I have calculated an R^2 value for the pre-inflection of 0.712. However, calculations of the R^2 value for the post-inflection points runs from a miserable 0.416 down to a disastrous value of 0.18. The only thing that can be determined from these trend lines is that anything post-inflection may be attributed to herd of elk migrating, or phase of the moon, or the phrenology of the author." (no offense meant).
Perhaps making inferences without supporting statistics is why many skeptics are raked over the coals. I await the next articles and their supporting evidence. Thank you, doc
"Looking at the data in Exh A, I have calculated an R^2 value for the pre-inflection of 0.712. However, calculations of the R^2 value for the post-inflection points runs from a miserable 0.416 down to a disastrous value of 0.18."
A person who contended this would be a complete idiot, and I would never listen to another thing they said. These are 'Variations Against Trend (Baseline)' charts - they have an inherent 'bias to R^2 fit'. Any lower R^2 or departure from fit indicates a SIGNAL, not the lack of one.
I think you are missing this, and the four points I made.
You just used the word Trend in your quotes. The trend line represents the linear interpolation of the data points. This is true no matter what signal you are trying to convey. Point 1 is an excellent example of where a regression is called for. Point 2 is what you are trying to convey, or signal. No problem.
In closing, if you leave the trend line out(post-inflection), you would have no concern about the R^2 value, and the non-statistics among us can make and see their own best fit. Your 'aha!' moment. If/when you are going to put a linear regression trend line(post-inflection) of the data points to prove your signal direction and magnitude, leaving out an R^2 value - even if it is worse than pre-inflection is a mistake. As noted, we expect the regression to get worse. But no matter the delta R^2, from pre and post-inflection, either do or don't for both.
Haveaniceday; doc :-)
Trend and 'linear fit' are not congruent, despite your insistence that they are. There exists such a thing called Non-Linear optimization (my Major is in this). It uses the Golden Section method to conduct regression/trend analysis.
As you can see below, gravity (no inflection, single function, and indeed a TREND) produces a trend in the motion of a planet, but if you place an R^2 on it the fit is going to be horrible. Does that mean that gravity does not exist!!!!!!!!!!?????
This is what you are saying - that gravity does not exist, because it doesn't fit an R^2 well.
https://theethicalskeptic.com/wp-content/uploads/2022/08/Gravity-does-not-exist.png