Total sum of squares Puns

Example: if you want to use 12ft, 16ft, & 20ft and your deck is 600 sq ft. Take 600 x 2.25 = 1,350. Now divide 1,350 by 48 (the sum of 12+16+20) which gives you 28.125. So, you’ll need 29 boards of each length of material to get the best of your staggered seams.

I've done several statistics courses in university and I'm starting to wonder why or what "sum of squares" is used for in tests like linear regression. What is particular useful about the "sum of squares"?

Hi folks! Ive got a question here asking what the estimated variance of the observations at the conditional mean is.

The setting is:

• simple linear regression y=a+bx with estimated coefficients a and b .
• given dataset with sample size n

I’ve calculated Total Sum of Square (TSS) by summing up the regression sum of squares and residuals sum of squares.

Should I just get the estimated variance by TSS/(n-1), which is equal to the total mean square? But I get confused on ‘at a conditional mean’ and I really wonder whether it brings any other constraint that I haven’t considered.

Plus the next question it asks is to calculate the TSS, which makes me more confused cuz I thought it was included in this question already!

Could you please give me some help? Lots of thanks in advance!

To be honest I can't really understand this question, let alone solving it for him. I find it weird. I just assumed that he thinks numbers of angles and sides are directly related in a way. Some of us were arguing that maybe it's just that 'a shape with 2 sides' simply doesn't and couldn't exist at all, because it wouldn't be a *shape*, it would be a straight line. Or that some kind of theorems are required to solve this. I personally think that it's something about geometry properties/ theorems that we forgot or don't know.

Can anyone help me and my friends? It's not a serious question. I'm sure it's more like a shower thought that he came up with, but I'd really appreciated it if you guys can help us dummies.

Just to clarify, the latter doesn’t imply dualistic conception of reality. Understanding that all energy, such as words, inherently exist as emanations of the source without modifying the essential nature of its non duality.

We know that a product of 2 sums of 2 squares is a sum of 2 squares.
m=x^2+y^2 n=z^2+t^2

mn=(xz-yt)^2+(xt+yz)^2

What I need:
- Is m*n is the hypotenuse of 2 primitive Pythagorean triples?

- does m*n have 2 representations as sums of 2 squares?

Example:
m=16+25, n=4+9, m*n=533

2 representations as a sum of 2 squares:
533 = 2^2+23^2

533 = 7^2+22^2
Pythagorean triples:

533^2 = 92^2+525^2

533^2 = 308^2+435^2

I know the formula for the total sum of squares, but the x values I'm using are in two different groups (for example one group is children aged 0-6 months and the other is 6-12 months, but the x is still the same) to calculate the mean of x do I just add them together or do I do the total sum of squares separately?

Thanks

Pville/RR area but don’t really mind driving if it saves me a few bucks, recently bought a handgun and I know as September you don’t necessarily need the LTC but I would still like to get one, but I’m new to all of this (still have to get a few more trips to the range under my belt) but what was the total sum of the process and what/when do you pay. Thank you in advance!

Continued from here

Thanks to Nitrome for the run and the assist.

Count using the sum of four squares, I personally use this site.

Next get is 13,000.

Hi all, I have a continuously differentiable strictly convex function v:R^2 --> R_+, like v(x, y) = z.

v is increasing in both its arguments, and has strictly negative second derivatives the cross-partial second derivatives are strictly positive.

QUESTION Is there anything I can say about the sign of v_{xx} - 2v_{xy} + v_{yy}?

I mention the "square" form because it sort of resembles a quadratic.

Thank you :)

Continued from here

Thanks to u/thenitromefan for the assist!

Did you know each number can be written as the sum of up to four squares? In this thread all you need to do is write each number as the sum of up to four square numbers. This tool should help you out.

Next get is at 11000.

I have a problem where I want to optimize a cost function that is a sum of squares of bilinear forms, where the vectors in the forms are the parameters I want to estimate.

For example, lets say we have 4 vectors: w, x, y, z, all 2 by 1 vectors that are constrained to be unit norm. I want to minimize this problem:

(w^T Q1 x)^2 + (y^T Q2 z)^2 + (w^T Q3 z)^2 + (x^T Q3 y)^2

here Q1, Q2, and Q3 are all fixed 2 by 2 matrices. This is the sum of squares of 4 different bilinear forms. I need to find w, x, y, and z that minimizes this problem.

I know how to create an iterative algorithm to solve this: e.g. when fixing all vectors but w, it can be shown that the solution to w is the smallest eigenvector of Q1 x x^T Q1^T + Q3 z z^T Q3^T . However, I want to know if it possible to arrive at a direct solution to this problem.

I'm looking at Griffith's Electrodynamics, problem 4.20 (a sphere of linear dielectric material has embedded within it a uniform free charge density.) I solved the potential just fine, but I'm stuck on this one small conceptual point that doesn't really have much to do with the solution itself but is something I was thinking about while working out the math because I like to visualize things in my head.

As far as I know, the total bound charge density should always sum to zero, and since the bound volume charge density in the case of constant P is zero, that must mean that the total surface-bound charge density also equals zero.

Yet, to the best of my knowledge, P is directed radially outward, and so the bound surface charge density of the sphere seems to me, at a glance, to be non-zero.

I know I'm missing something silly. Can someone explain what's wrong with my reasoning?

EDIT: I'm not sure if it matters, but I'm self-studying physics (I took a three-semester college physics course and the required calculus / linear algebra before graduating many years ago and am now trying to continue the journey on my own.)

EDIT 2: Solved! Thank you, u/pinkpanzer101! P is not constant, so there's a divergence that results in a volume bound charge density that cancels out the surface bound charge.

Is he trying to scam? Edit: four wheeler only.no two wheeler.

Update : So the instructor is saying like day by day,the amount get incremented so that it may reach paying 50000/- bucks to obtain license in near future.RTO inspector's are imposing new rules like student should provide proof of minimum number of classes attended in driving school (i guess 25- 29) during DL test.What led to these rules?

I've spent a lot of time looking through websites for these comprehensive lists, and finally found some amazing sites that I think will benefit everyone.

Here is all Eminem songs and features from 1988-2021. Scroll down after the list of his albums and you have a year-wise list of all songs and guest features by Eminem

https://genius-com.cdn.ampproject.org/v/s/genius.com/amp/Eminem-eminem-discography-list-annotated?amp_js_v=a6&amp_gsa=1&usqp=mq331AQKKAFQArABIIACAw%3D%3D#aoh=16338375410598&referrer=https%3A%2F%2Fwww.google.com&amp_tf=From%20%251%24s&ampshare=https%3A%2F%2Fgenius.com%2FEminem-eminem-discography-list-annotated

If you think the year-wise is a little messy and wanna cross-check the songs with their respective albums, you can do that on the site below here:

https://teaandweed.com/eminem-discography/

Below is a link to a comprehensive list of all Eminem's beefs, with a detailed list of the disstracks made by the person he beefed with and Eminem's disstracks against said rapper:

https://www.nme.com/blogs/nme-blogs/eminem-vs-everyone-comprehensive-list-slim-shady-lyrical-feuds-beefs-2561575

And finally a spreadsheet list of most of Eminem leaked/unreleased tracks and features(containing a link to the track for those tracks that are actually available online):

https://docs.google.com/spreadsheets/u/0/d/1zPw40UxQTnQ5q7SGjqPaHx-5YvjTKZFdmaierURfDV8/htmlview#gid=0

This is all that I have managed to collect, feel free to comment on this thread or DM me with any better lists you may have.

I'm watching regiments wander off from combat and seeing many small battles playing out while heavy-hitting units refuse to join.

It got me thinking about how the mapping works. Is it possible to program a bunch of calculations like units proximity to each other, characters, masses of units, unit power, and test the heck out of it so that missiles units missile, spearmen guard flanks and reinforce swordsmen, cavalry looks for open space and opportunities to hit skirmishers, and characters cast spells or use abilities when enemy units blob up.

This might already be happening and the technology used to do this is limited, or maybe it's the pathing that skews things due to walls and city features.

Obviously I'm talking out of my tuckus but I'm so curious how the programming works for games like Total War and if, given the long history of video games not quite nailing AI on release, there's some way to open up the process and allow great ideas float to the top for implementation?

Hi all,

New to excel and need help making a formula.

I have a large data set with a value in the columns, and a corresponding start and end date for each value.

Example

I need to get the total exposure (value in apm multiplied by number of days) at 3 months intervals for each row. (i.e. each row is one subject and each apm {1,2,3} is a different exposure)

If two columns in one row overlap in that time period then the two totals are combined for those overlapping days for that 3 month interval. If for example there is only 4 months of exposure, the 6 month interval will include just that extra 1 month of exposure.

Example with the 3rd row done out

Hope I've explained that at all clearly and thanks so much in advance for any help, very appreciated.

This may be an intuitive question, but please indulge me.

I'm currently working on a side project with random numbers where one needs to achieve a given total, T, rolling a fair die with s sides. So, if we set T=10 and s=4, the question I'm asking is 'How many rolls is one expected to roll to achieve at least T?'.

So in this case, you could roll a 1, 2, 3, or 4. One your second roll, you could roll those same numbers, summing them, thus rendering your totals to:

1: 2, 3, 4, 5

2: 3, 4, 5, 6

3: 4, 5, 6, 7

4: 5, 6, 7, 8

Rolling again, you'd get

2: 3, 4, 5, 6

3: 4, 5, 6, 7

4: 5, 6, 7, 8

5: 6, 7, 8, 9

6: 7, 8, 9, 10

7: 8, 9, 10, 11

8: 9, 10, 11, 12

At this point (Roll 3), we've succeeded in ~21.4% of cases. We could keep rolling, expanding this chart until there is no value <T.

Is there an easy formula to solve this question generally? Obviously, the most we could roll is a string of 1s such that the number of rolls is just equal to T, but the largest number (s) is variable.

So basically, sqrt(morale bonus 1^2 + morale bonus 2^2 ... + morale bonus n^2 ).

#What this means for gameplay

• Obviously, morale bonuses have diminishing returns.
• Smaller numbers are less resilient to these diminishing returns.
• A single large morale boost is drastically more effective than many small morale boosts.
• Your total morale bonus will always be at least as large as the biggest boost you have.
• Optimism and Bad Temper still work the same as expected.

If you have a morale boost of 12, you get a total bonus of 12. If you add a morale boost of 5 to that, you get a total bonus of 13. If instead, you have just a morale boost of 17, you get a morale bonus of 17.

I've created a Desmos graph here, for you to see and toy with the numbers yourself.

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#What this means for math nerds

This is the the Euclidean norm, or Euclidean length, or magnitude of the vector of morale boosts. Essentially, in a space with as many dimensions as one has morale boosts, how long a line would be, with the lengths in each dimension determined by the morale boosts.

In simpler terms, if you only have two morale boosts, the total bonus is the hypotenuse of a right triangle, where the two other sides or the two morale boosts.

From here

Thanks to u/TDs_not_VDs for the assist and TNF for counting most of the last thread.

Next get at 12,000

Happy counting!