x’ forecast only on HP-32E

[C.Ret]

(06-20-2023 09:12 PM)brouhaha Wrote:  

(06-20-2023 12:56 PM)Dave Britten Wrote:  I always thought it was kind of odd they included it on the 12C but not the 11C or 15C.

"Life is short and ROM is full."
- Bill Wickes

But also there aren't extra key assignments available on the 11C and 15C.

Hi,

I like this quote but wouldn't it be from Wiliam C Wickes? Was Bill a joke-nickname?

Otherwise, the HP-15C actually lacks keys to put the two estimation x^ and y^ (not to be confuse with any forecast - only linear estimation link to the actual linear regression).


With the statistic accumulated in the HP-15C registers, both estimated values for x and y, denoted x^and y^, can be calculated without any program or any register substitution:

An estimated value for x (denoted x^) can be obtained from the sequence:

1. Press f ( L.R. )
2. Key in the know y-value
3. Press (X↔Y) ( - ) (X↔Y) ( ÷ )

An estimated value for y (denoted y^) can be obtained from one of the sequences:

1. Press f ( L.R. )(X↔Y)
2. Key in the know x-value
3. Press ( × ) ( + )

Alternatively

1. Key in the know x-value
2. Press f ( y^.r )

« Le statisticien est un homme qui fait un calcul juste en partant de prémices douteuses pour aboutir à un résultat faux. »
Jean Delacour
"The statistician is a person who performs accurate calculations based on approximate and debatable data, ultimately leading to an incorrect result."
Dubious Personal Translation.

Unlike forecasts, estimates don't have to worry about all those pesky things like data consistency, biases, measurement errors, distributions or dispersions shapes, theoretical vs empirical laws, probabilities, linearity...

Facts are stubborn, but statistics are more pliable.
Mark Twain

[Joe Horn]

(06-24-2023 08:17 PM)C.Ret Wrote:  

(06-20-2023 09:12 PM)brouhaha Wrote:  "Life is short and ROM is full."
- Bill Wickes

I like this quote but wouldn't it be from Wiliam C Wickes? Was Bill a joke-nickname?

<TMI> Although "William" is his legal and formal name, he calls himself "Bill" in all informal settings, and everybody who knows him calls him "Bill". In the "Credits" section of the books by James Donnelly (who always calls himself "Jim"), he calls him "Bill Wickes". It's the same as the way that my legal and formal name is "Joseph", but I call myself "Joe" and everybody who knows me calls me "Joe". Yes, I suppose that these are called "nicknames", but please note that they are polite nicknames, with no implications of being a joke or lacking any respect. At least in American culture there is a difference between polite nicknames (which carry the same respect as the formal name) and joke nicknames (which span the huge range from terms of endearment to intentionally offensive insults). Shortened names (e.g., "Joe" for "Joseph", "Bill" for "William", "Sam" for "Samuel", "Chris" for "Christopher", and so on) are usually polite nicknames, at least in the USA. </TMI>

[Valentin Albillo]

(06-24-2023 09:26 PM)Joe Horn Wrote:  Shortened names (e.g., "Joe" for "Joseph", "Bill" for "William", "Sam" for "Samuel", "Chris" for "Christopher", and so on) are usually polite nicknames, at least in the USA.

"Sam" is also a common polite nickname for "Samantha" as well. And we have lots of those polite nicknames in Spain, too, such as Pepe (José), Paco (Francisco), Pili (Pilar), Toñi (Antonia), etc. though they're rarely used with authorities, i.e. people in the US will call the current POTUS "Joe" with no disrespect whatsoever but in Spain we'd never address the Pope as "el Papa Paco".

V.

[C.Ret]

Thanks Joe for that clarification.

This cultural fact had completely escaped from me and I hadn't realized that a nickname is used very respectfully by anyone, from close relatives up to co-workers and collaborators. There are parts of the world where nicknames, especially those given to authorities and managers, are most often pejorative or scoffer. I live and work in these types of part of the world.


Thank you Valentin,

It's true that there are plenty of nicknames for everyday life. And that makes sense.
I should have remembered that Bill is the diminutive of William. And I should have realize that in the US, one prefers to be called Bill than William, which sound far too british.

[Namir]

Projecting x onto y' (or y-hat) is not the whole picture! The value for y-hat is the mean of a range defined by a confidence interval. So x is related to yhat residing in a confidence interval. In order words x is related to a set of y values! This is the more complete picture. Calculating x-hat from y (or should I say y-hat) does not give x-hat residing in an x-oriented confidence interval.

This is what I learned from my 1979 stat course teacher. He had a PhD in chemical engineering from MIT and was an HP-65 calculator toting teacher! He enjoyed seeing my HP-67 and was pleased to learn that I had learned statistics from the HP calculators stat pacs!

Namir

[Nigel (UK)]

I have to confess that I don't see I am committing any heresy by changing \(y = a + bx\) into \(x = (y-a)/b\)! In some cases - for example, unit conversions - both variables have the same "character". Any uncertainty in a temperature measurement in degrees Celsius corresponds to an exactly equivalent uncertainty when measuring the same temperature in degrees Fahrenheit. Inverting the formula in such cases is surely fine.

In other cases - for example, how population \(P\) changes with time \(t\) - the two variables are not equivalent. Not only is population harder to measure than what year it is, but its value cannot be chosen freely. It also depends on factors other than time. Even so, if I decide to fit a set of \((t,P)\) measurements to an equation \(P=a+bt+\epsilon\), where \(\epsilon\) is normally distributed with zero mean and fixed variance, I can get best estimates for \(a\) and \(b\) and then invert the equation again to get
\[t = {P - a- \epsilon\over b}.\]
This gives me a value for \(t\) along with an idea of the uncertainty in the answer.

Best of all, fire up a MCMC (Markov Chain Monte Carlo) Bayes engine and feed it with the \(t,P\) measurements and the model equation. In this situation, the "error" function \(\epsilon\) doesn't have to be normal and its parameters (e.g., variance) can be fitted from the data. You end up with a list of ten thousand (for example) sets of values for \(a\), \(b\), and the error function parameters. You can use each of these sets to calculate a spread of values for \(t\) from \(P\), and then combine them all into one. No current HP calculator does this out of the box, I fear!

Disclaimer: I am not a statistician, but I have read a few books.

Nigel (UK)

[rawi]

Hi Nigel,

in your equation, if Epsilon has a normal distribution with mean zero and standard deviation s your x has as well a normal distribution with mean zero and standard deviation s/b. The point is that x is not a random variable and does not have a distribution. That is why we minimize in regression analysis the sum of squares in the direction of the y axis. If x and y both have a distributuion you need another model and you will get a different beta. You can read about this here: https://en.wikipedia.org/wiki/Errors-in-...les_models

[Nigel (UK)]

(06-28-2023 01:37 PM)rawi Wrote:  Hi Nigel,

in your equation, if Epsilon has a normal distribution with mean zero and standard deviation s your x has as well a normal distribution with mean zero and standard deviation s/b. The point is that x is not a random variable and does not have a distribution. That is why we minimize in regression analysis the sum of squares in the direction of the y axis. If x and y both have a distributuion you need another model and you will get a different beta. You can read about this here: https://en.wikipedia.org/wiki/Errors-in-...les_models

Although x may not be a random variable, my knowledge of its value (given a definite value of y) is uncertain. I take the Bayesian view that the probability distribution for such a variable is a reflection of this uncertainty in my knowledge; indeed, this (or something close) is the Bayesian definition of probability. (Heresy? Surely not!)

I agree that the equation in the second paragraph of my previous post is unlikely to give the correct (Bayesian) answer - using precise values for a and b will underestimate the uncertainty in x - but the approach in the third paragraph should work, I think.

As I said, I am not remotely an expert on this subject!

Nigel (UK)