Mixing
Ordinary Least Squares Regression
Clash Royale CLAN TAG#URR8PPP
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I am quite surprised that a variant of linear regression has been proposed for a challenge, whereas an estimation via ordinary least squares regression has not, despite the fact the this is arguably the most widely used method in applied economics, biology, psychology, and social sciences!
For details, check out the Wikipedia page on OLS. To keep things concise, suppose one has a model:
where all right-hand side X variables—regressors—are linearly independent and are assumed to be exogenous (or at least uncorrelated) to the model error U. Then you solve the problem
on a sample of size n, given observations
The OLS solution to this problem as a vector looks like
where Y is the first column of the input matrix and X is a matrix made of remaining columns. This solution can be obtained via many numerical methods (matrix inversion, QR decomposition, Cholesky decomposition etc.), so pick your favourite!
Of course, econometricians prefer slightly different notation, but let’s just ignore them. — Do you know what econometricians use as a contraceptive? — Their personalities! (Don’t worry, I can say that, I am an econometrician...)
Non other than Gauss himself is watching you from the skies, so do not disappoint one of the greatest mathematicians of all times and write the shortest code possible.
Task
Given the observations in a matrix form as shown above, estimate the coefficients of the linear regression model via OLS.
Input
A matrix of values. The first column is always Y[1], ..., Y[n], the second column is X1[1], ..., X1[n], the next one is X2[1], ..., X2[n] etc.
NB. In statistics, regressing on a constant is widely used. This means that the model is Y = b0 + U, and the OLS estimate of b0 is the sample average of Y. In this case, the input is just a matrix with one column, Y.
You can safely assume that the variables are not exactly collinear, so the matrices above are invertible. In case your language cannot invert matrices with condition numbers larger than a certain threshold, state it explicitly, and provide a unique return value (that cannot be confused with output in case of success) denoting that the system seems to be computationally singular (S or any other unambiguous characters).
Output
OLS estimates of beta_0, ..., beta_k from a linear regression model in an unambiguous format or an indication that your language could not solve the system.
Challenge rules
- I/O formats are flexible. A matrix can be several lines of space-delimited numbers separated by newlines, or an array of row vectors, or an array of column vectors etc.
- This is code-golf, so shortest answer in bytes wins.
- Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lmin R is not a valid answer because it expects a different kind of input.
Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs.
Default loopholes are forbidden.
Test cases
[[4,5,6],[1,2,3]]→ output:[3,1].[[5.5,4.1,10.5,7.7,6.6,7.2],[1.9,0.4,5.6,3.3,3.8,1.7],[4.2,2.2,3.2,3.2,2.5,6.6]]→ output:[2.1171050,1.1351122,0.4539268].[[1,-2,3,-4],[1,2,3,4],[1,2,3,4.000001]]→ output:[-1.3219977,6657598.3906250,-6657597.3945312]orS(any code for a computationally singular system).[[1,2,3,4,5]]→ output:3.
Bonus points (to your karma, not to your byte count) if your code can solve very ill-conditioned (quasi-multicollinear) problems (e. g. if you throw in an extra zero in the decimal part of X2[4] in Test Case 3) with high precision.
For fun: you can implement estimation of standard errors (White’s sandwich form or the simplified homoskedastic version) or any other kind of post-estimation diagnostics to amuse yourself if your language has built-in tools for that (I am looking at you, R, Python and Julia users). In other words, if your language allows to do cool stuff with regression objects in few bytes, you can show it!
code-golf matrix statistics
asked 2 hours ago
Andreï Kostyrka
1,149617
add a comment |Â
up vote
1
down vote
favorite
I am quite surprised that a variant of linear regression has been proposed for a challenge, whereas an estimation via ordinary least squares regression has not, despite the fact the this is arguably the most widely used method in applied economics, biology, psychology, and social sciences!
For details, check out the Wikipedia page on OLS. To keep things concise, suppose one has a model:
where all right-hand side X variables—regressors—are linearly independent and are assumed to be exogenous (or at least uncorrelated) to the model error U. Then you solve the problem
on a sample of size n, given observations
The OLS solution to this problem as a vector looks like
where Y is the first column of the input matrix and X is a matrix made of remaining columns. This solution can be obtained via many numerical methods (matrix inversion, QR decomposition, Cholesky decomposition etc.), so pick your favourite!
Of course, econometricians prefer slightly different notation, but let’s just ignore them. — Do you know what econometricians use as a contraceptive? — Their personalities! (Don’t worry, I can say that, I am an econometrician...)
Non other than Gauss himself is watching you from the skies, so do not disappoint one of the greatest mathematicians of all times and write the shortest code possible.
Task
Given the observations in a matrix form as shown above, estimate the coefficients of the linear regression model via OLS.
Input
A matrix of values. The first column is always Y[1], ..., Y[n], the second column is X1[1], ..., X1[n], the next one is X2[1], ..., X2[n] etc.
NB. In statistics, regressing on a constant is widely used. This means that the model is Y = b0 + U, and the OLS estimate of b0 is the sample average of Y. In this case, the input is just a matrix with one column, Y.
You can safely assume that the variables are not exactly collinear, so the matrices above are invertible. In case your language cannot invert matrices with condition numbers larger than a certain threshold, state it explicitly, and provide a unique return value (that cannot be confused with output in case of success) denoting that the system seems to be computationally singular (S or any other unambiguous characters).
Output
OLS estimates of beta_0, ..., beta_k from a linear regression model in an unambiguous format or an indication that your language could not solve the system.
Challenge rules
- I/O formats are flexible. A matrix can be several lines of space-delimited numbers separated by newlines, or an array of row vectors, or an array of column vectors etc.
- This is code-golf, so shortest answer in bytes wins.
- Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lmin R is not a valid answer because it expects a different kind of input.
Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs.
Default loopholes are forbidden.
Test cases
[[4,5,6],[1,2,3]]→ output:[3,1].[[5.5,4.1,10.5,7.7,6.6,7.2],[1.9,0.4,5.6,3.3,3.8,1.7],[4.2,2.2,3.2,3.2,2.5,6.6]]→ output:[2.1171050,1.1351122,0.4539268].[[1,-2,3,-4],[1,2,3,4],[1,2,3,4.000001]]→ output:[-1.3219977,6657598.3906250,-6657597.3945312]orS(any code for a computationally singular system).[[1,2,3,4,5]]→ output:3.
Bonus points (to your karma, not to your byte count) if your code can solve very ill-conditioned (quasi-multicollinear) problems (e. g. if you throw in an extra zero in the decimal part of X2[4] in Test Case 3) with high precision.
For fun: you can implement estimation of standard errors (White’s sandwich form or the simplified homoskedastic version) or any other kind of post-estimation diagnostics to amuse yourself if your language has built-in tools for that (I am looking at you, R, Python and Julia users). In other words, if your language allows to do cool stuff with regression objects in few bytes, you can show it!
code-golf matrix statistics
asked 2 hours ago
Andreï Kostyrka
1,149617
What about built-ins, does it have to be an original solver code, or using a built-in is OK?
– Kirill L.
1 hour ago
@KirillL. Added this rule: Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answerlmin R is not a valid answer because it expects a different kind of input.
– Andreï Kostyrka
1 hour ago
Well, I guessed that :) Still a bit unsure about I/O though. Is this valid? - takes input as data frame, and returns nothing with debug info on singular case
– Kirill L.
1 hour ago
1
@KirillL. Yes, of course! Post it! (Optionally: and watch your clever answer being beaten by someone’s Pyth or MATL string of seemingly random characters.) Just specify that the input format is this:as.data.frame(matrix(c(Y,X1,...),n))wherenindicates the number of observations.
– Andreï Kostyrka
1 hour ago
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I am quite surprised that a variant of linear regression has been proposed for a challenge, whereas an estimation via ordinary least squares regression has not, despite the fact the this is arguably the most widely used method in applied economics, biology, psychology, and social sciences!
For details, check out the Wikipedia page on OLS. To keep things concise, suppose one has a model:
where all right-hand side X variables—regressors—are linearly independent and are assumed to be exogenous (or at least uncorrelated) to the model error U. Then you solve the problem
on a sample of size n, given observations
The OLS solution to this problem as a vector looks like
where Y is the first column of the input matrix and X is a matrix made of remaining columns. This solution can be obtained via many numerical methods (matrix inversion, QR decomposition, Cholesky decomposition etc.), so pick your favourite!
Of course, econometricians prefer slightly different notation, but let’s just ignore them. — Do you know what econometricians use as a contraceptive? — Their personalities! (Don’t worry, I can say that, I am an econometrician...)
Non other than Gauss himself is watching you from the skies, so do not disappoint one of the greatest mathematicians of all times and write the shortest code possible.
Task
Given the observations in a matrix form as shown above, estimate the coefficients of the linear regression model via OLS.
Input
A matrix of values. The first column is always Y[1], ..., Y[n], the second column is X1[1], ..., X1[n], the next one is X2[1], ..., X2[n] etc.
NB. In statistics, regressing on a constant is widely used. This means that the model is Y = b0 + U, and the OLS estimate of b0 is the sample average of Y. In this case, the input is just a matrix with one column, Y.
You can safely assume that the variables are not exactly collinear, so the matrices above are invertible. In case your language cannot invert matrices with condition numbers larger than a certain threshold, state it explicitly, and provide a unique return value (that cannot be confused with output in case of success) denoting that the system seems to be computationally singular (S or any other unambiguous characters).
Output
OLS estimates of beta_0, ..., beta_k from a linear regression model in an unambiguous format or an indication that your language could not solve the system.
Challenge rules
- I/O formats are flexible. A matrix can be several lines of space-delimited numbers separated by newlines, or an array of row vectors, or an array of column vectors etc.
- This is code-golf, so shortest answer in bytes wins.
- Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lmin R is not a valid answer because it expects a different kind of input.
Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs.
Default loopholes are forbidden.
Test cases
[[4,5,6],[1,2,3]]→ output:[3,1].[[5.5,4.1,10.5,7.7,6.6,7.2],[1.9,0.4,5.6,3.3,3.8,1.7],[4.2,2.2,3.2,3.2,2.5,6.6]]→ output:[2.1171050,1.1351122,0.4539268].[[1,-2,3,-4],[1,2,3,4],[1,2,3,4.000001]]→ output:[-1.3219977,6657598.3906250,-6657597.3945312]orS(any code for a computationally singular system).[[1,2,3,4,5]]→ output:3.
Bonus points (to your karma, not to your byte count) if your code can solve very ill-conditioned (quasi-multicollinear) problems (e. g. if you throw in an extra zero in the decimal part of X2[4] in Test Case 3) with high precision.
For fun: you can implement estimation of standard errors (White’s sandwich form or the simplified homoskedastic version) or any other kind of post-estimation diagnostics to amuse yourself if your language has built-in tools for that (I am looking at you, R, Python and Julia users). In other words, if your language allows to do cool stuff with regression objects in few bytes, you can show it!
code-golf matrix statistics
asked 2 hours ago
Andreï Kostyrka
1,149617
I am quite surprised that a variant of linear regression has been proposed for a challenge, whereas an estimation via ordinary least squares regression has not, despite the fact the this is arguably the most widely used method in applied economics, biology, psychology, and social sciences!
For details, check out the Wikipedia page on OLS. To keep things concise, suppose one has a model:
where all right-hand side X variables—regressors—are linearly independent and are assumed to be exogenous (or at least uncorrelated) to the model error U. Then you solve the problem
on a sample of size n, given observations
The OLS solution to this problem as a vector looks like
where Y is the first column of the input matrix and X is a matrix made of remaining columns. This solution can be obtained via many numerical methods (matrix inversion, QR decomposition, Cholesky decomposition etc.), so pick your favourite!
Of course, econometricians prefer slightly different notation, but let’s just ignore them. — Do you know what econometricians use as a contraceptive? — Their personalities! (Don’t worry, I can say that, I am an econometrician...)
Non other than Gauss himself is watching you from the skies, so do not disappoint one of the greatest mathematicians of all times and write the shortest code possible.
Task
Given the observations in a matrix form as shown above, estimate the coefficients of the linear regression model via OLS.
Input
A matrix of values. The first column is always Y[1], ..., Y[n], the second column is X1[1], ..., X1[n], the next one is X2[1], ..., X2[n] etc.
NB. In statistics, regressing on a constant is widely used. This means that the model is Y = b0 + U, and the OLS estimate of b0 is the sample average of Y. In this case, the input is just a matrix with one column, Y.
You can safely assume that the variables are not exactly collinear, so the matrices above are invertible. In case your language cannot invert matrices with condition numbers larger than a certain threshold, state it explicitly, and provide a unique return value (that cannot be confused with output in case of success) denoting that the system seems to be computationally singular (S or any other unambiguous characters).
Output
OLS estimates of beta_0, ..., beta_k from a linear regression model in an unambiguous format or an indication that your language could not solve the system.
Challenge rules
- I/O formats are flexible. A matrix can be several lines of space-delimited numbers separated by newlines, or an array of row vectors, or an array of column vectors etc.
- This is code-golf, so shortest answer in bytes wins.
- Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lmin R is not a valid answer because it expects a different kind of input.
Standard rules apply for your answer, so you are allowed to use STDIN/STDOUT, functions/method with the proper parameters and return-type, full programs.
Default loopholes are forbidden.
Test cases
[[4,5,6],[1,2,3]]→ output:[3,1].[[5.5,4.1,10.5,7.7,6.6,7.2],[1.9,0.4,5.6,3.3,3.8,1.7],[4.2,2.2,3.2,3.2,2.5,6.6]]→ output:[2.1171050,1.1351122,0.4539268].[[1,-2,3,-4],[1,2,3,4],[1,2,3,4.000001]]→ output:[-1.3219977,6657598.3906250,-6657597.3945312]orS(any code for a computationally singular system).[[1,2,3,4,5]]→ output:3.
Bonus points (to your karma, not to your byte count) if your code can solve very ill-conditioned (quasi-multicollinear) problems (e. g. if you throw in an extra zero in the decimal part of X2[4] in Test Case 3) with high precision.
For fun: you can implement estimation of standard errors (White’s sandwich form or the simplified homoskedastic version) or any other kind of post-estimation diagnostics to amuse yourself if your language has built-in tools for that (I am looking at you, R, Python and Julia users). In other words, if your language allows to do cool stuff with regression objects in few bytes, you can show it!
code-golf matrix statistics
code-golf matrix statistics
asked 2 hours ago
Andreï Kostyrka
1,149617
asked 2 hours ago
Andreï Kostyrka
1,149617
edited 1 hour ago
asked 2 hours ago
Andreï Kostyrka
1,149617
asked 2 hours ago
Andreï Kostyrka
1,149617
asked 2 hours ago
Andreï Kostyrka
1,149617
1,149617
What about built-ins, does it have to be an original solver code, or using a built-in is OK?
– Kirill L.
1 hour ago
@KirillL. Added this rule: Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answerlmin R is not a valid answer because it expects a different kind of input.
– Andreï Kostyrka
1 hour ago
Well, I guessed that :) Still a bit unsure about I/O though. Is this valid? - takes input as data frame, and returns nothing with debug info on singular case
– Kirill L.
1 hour ago
1
@KirillL. Yes, of course! Post it! (Optionally: and watch your clever answer being beaten by someone’s Pyth or MATL string of seemingly random characters.) Just specify that the input format is this:as.data.frame(matrix(c(Y,X1,...),n))wherenindicates the number of observations.
– Andreï Kostyrka
1 hour ago
add a comment |Â
What about built-ins, does it have to be an original solver code, or using a built-in is OK?
– Kirill L.
1 hour ago
@KirillL. Added this rule: Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answerlmin R is not a valid answer because it expects a different kind of input.
– Andreï Kostyrka
1 hour ago
Well, I guessed that :) Still a bit unsure about I/O though. Is this valid? - takes input as data frame, and returns nothing with debug info on singular case
– Kirill L.
1 hour ago
1
@KirillL. Yes, of course! Post it! (Optionally: and watch your clever answer being beaten by someone’s Pyth or MATL string of seemingly random characters.) Just specify that the input format is this:as.data.frame(matrix(c(Y,X1,...),n))wherenindicates the number of observations.
– Andreï Kostyrka
1 hour ago
What about built-ins, does it have to be an original solver code, or using a built-in is OK?
– Kirill L.
1 hour ago
What about built-ins, does it have to be an original solver code, or using a built-in is OK?
– Kirill L.
1 hour ago
@KirillL. Added this rule: Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lm in R is not a valid answer because it expects a different kind of input.– Andreï Kostyrka
1 hour ago
@KirillL. Added this rule: Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lm in R is not a valid answer because it expects a different kind of input.– Andreï Kostyrka
1 hour ago
Well, I guessed that :) Still a bit unsure about I/O though. Is this valid? - takes input as data frame, and returns nothing with debug info on singular case
– Kirill L.
1 hour ago
Well, I guessed that :) Still a bit unsure about I/O though. Is this valid? - takes input as data frame, and returns nothing with debug info on singular case
– Kirill L.
1 hour ago
1
1
@KirillL. Yes, of course! Post it! (Optionally: and watch your clever answer being beaten by someone’s Pyth or MATL string of seemingly random characters.) Just specify that the input format is this:
as.data.frame(matrix(c(Y,X1,...),n)) where n indicates the number of observations.– Andreï Kostyrka
1 hour ago
@KirillL. Yes, of course! Post it! (Optionally: and watch your clever answer being beaten by someone’s Pyth or MATL string of seemingly random characters.) Just specify that the input format is this:
as.data.frame(matrix(c(Y,X1,...),n)) where n indicates the number of observations.– Andreï Kostyrka
1 hour ago
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
4
down vote
R, 34 bytes
function(x)try(lm(V1~.,x,si=F)$co)
Try it online!
Notes:
- Takes input as a data frame (which is what
lmexpects) lmwould in principle work even without formula with input of indicated format, but it is needed for the constant regression casesi=F, short forsingular.ok=FALSE
throws an error for singular case, which is then caught bytry, eventually returning nothing and printing the error as debug info.
Otherwise, the regression would actually return some output, but not the
expected one.
answered 1 hour ago
Kirill L.
2,6061116
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
4
down vote
R, 34 bytes
function(x)try(lm(V1~.,x,si=F)$co)
Try it online!
Notes:
- Takes input as a data frame (which is what
lmexpects) lmwould in principle work even without formula with input of indicated format, but it is needed for the constant regression casesi=F, short forsingular.ok=FALSE
throws an error for singular case, which is then caught bytry, eventually returning nothing and printing the error as debug info.
Otherwise, the regression would actually return some output, but not the
expected one.
answered 1 hour ago
Kirill L.
2,6061116
add a comment |Â
up vote
4
down vote
R, 34 bytes
function(x)try(lm(V1~.,x,si=F)$co)
Try it online!
Notes:
- Takes input as a data frame (which is what
lmexpects) lmwould in principle work even without formula with input of indicated format, but it is needed for the constant regression casesi=F, short forsingular.ok=FALSE
throws an error for singular case, which is then caught bytry, eventually returning nothing and printing the error as debug info.
Otherwise, the regression would actually return some output, but not the
expected one.
answered 1 hour ago
Kirill L.
2,6061116
add a comment |Â
up vote
4
down vote
up vote
4
down vote
R, 34 bytes
function(x)try(lm(V1~.,x,si=F)$co)
Try it online!
Notes:
- Takes input as a data frame (which is what
lmexpects) lmwould in principle work even without formula with input of indicated format, but it is needed for the constant regression casesi=F, short forsingular.ok=FALSE
throws an error for singular case, which is then caught bytry, eventually returning nothing and printing the error as debug info.
Otherwise, the regression would actually return some output, but not the
expected one.
answered 1 hour ago
Kirill L.
2,6061116
R, 34 bytes
function(x)try(lm(V1~.,x,si=F)$co)
Try it online!
Notes:
- Takes input as a data frame (which is what
lmexpects) lmwould in principle work even without formula with input of indicated format, but it is needed for the constant regression casesi=F, short forsingular.ok=FALSE
throws an error for singular case, which is then caught bytry, eventually returning nothing and printing the error as debug info.
Otherwise, the regression would actually return some output, but not the
expected one.
answered 1 hour ago
Kirill L.
2,6061116
edited 1 hour ago
answered 1 hour ago
Kirill L.
2,6061116
answered 1 hour ago
Kirill L.
2,6061116
answered 1 hour ago
Kirill L.
2,6061116
2,6061116
add a comment |Â
add a comment |Â
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What about built-ins, does it have to be an original solver code, or using a built-in is OK?
– Kirill L.
1 hour ago
@KirillL. Added this rule: Built-in functions are allowed as long as they are tweaked to produce a solution given the input matrix as an argument. That is, the two-byte answer
lmin R is not a valid answer because it expects a different kind of input.– Andreï Kostyrka
1 hour ago
Well, I guessed that :) Still a bit unsure about I/O though. Is this valid? - takes input as data frame, and returns nothing with debug info on singular case
– Kirill L.
1 hour ago
1
@KirillL. Yes, of course! Post it! (Optionally: and watch your clever answer being beaten by someone’s Pyth or MATL string of seemingly random characters.) Just specify that the input format is this:
as.data.frame(matrix(c(Y,X1,...),n))wherenindicates the number of observations.– Andreï Kostyrka
1 hour ago