topic Multiple linear regressions within a dataset in Statistical Procedures

Multiple linear regressions within a dataset

svw1900 — Sat, 06 Oct 2018 12:33:53 GMT

Hi everyone,

I am using SAS University Edition and have a question regarding a regression analysis, which is probably easy to solve but I am new to SAS and did not found a particular solution for this (probably because I had not a real clue of how to find this).

I have a dataset which looks like this:

Year Stock_Identifier Y_Var X_Var1

2005 1 0,3 0,1

2006 1 0,4 0,2

2007 1 0,5 0,15

2008 1 0,6 0,25

2005 2 0,3 0,3

2006 2 0,3 0,4

2007 2 0,5 0,4

2008 2 0,4 0,5

What I need is a linear regression which tells me the correlation between Y and X1 (in the real dataset, I have some more X-Var but that should not be a problem). A normal linear regression would, I think, ignore the stock identifiers and just compare Y and X. That's where I need you. The regression does only make sense at the level of the stock, so in this case there should be one regression for stock 1 and its data points between 2005 and 2008 and the next one for the second stock. At the end, however, I need a "normal" regression output table aggregated at the level of the whole dataset.

I hope that this is clear and maybe it's a stupid question (sorry for that), but I am really thankful for your input (optimally you could even explain me the steps you take, because I am really new to SAS :-)).

Kind regards

Re: Multiple linear regressions within a dataset

PaigeMiller — Sat, 06 Oct 2018 13:15:33 GMT

proc sort data=have;
    by stock_identifier;
run;
proc reg data=have;
    by stock_identifier;
    model y_var = x_var1;
run;
quit;

I did not include a response to this part of your question:

At the end, however, I need a "normal" regression output table aggregated at the level of the whole dataset.

because I'm not sure what you mean.

Re: Multiple linear regressions within a dataset

Reeza — Sat, 06 Oct 2018 13:14:43 GMT

Try using a Task and it will generate the code.

Place stick in the GROUP ANALYSIS BY section.

https://documentation.sas.com/?activeCdc=webeditorcdc&cdcId=sasstudiocdc&cdcVersion=3.7&docsetId=webeditorref&docsetTarget=p1gb066aizom8ln1a324xn0g7f8m.htm&locale=en

As to how to combine them into one output, what’s the math behind that?

@svw1900 wrote:

Hi everyone,

I am using SAS University Edition and have a question regarding a regression analysis, which is probably easy to solve but I am new to SAS and did not found a particular solution for this (probably because I had not a real clue of how to find this).

I have a dataset which looks like this:

Year      Stock_Identifier       Y_Var       X_Var1

2005              1                       0,3            0,1

2006              1                       0,4            0,2

2007              1                       0,5            0,15

2008              1                       0,6            0,25

2005              2                       0,3            0,3

2006              2                       0,3            0,4

2007              2                       0,5            0,4

2008              2                       0,4            0,5

What I need is a linear regression which tells me the correlation between Y and X1 (in the real dataset, I have some more X-Var but that should not be a problem). A normal linear regression would, I think, ignore the stock identifiers and just compare Y and X. That's where I need you. The regression does only make sense at the level of the stock, so in this case there should be one regression for stock 1 and its data points between 2005 and 2008 and the next one for the second stock. At the end, however, I need a "normal" regression output table aggregated at the level of the whole dataset.

I hope that this is clear and maybe it's a stupid question (sorry for that), but I am really thankful for your input (optimally you could even explain me the steps you take, because I am really new to SAS :-)).

Kind regards

Re: Multiple linear regressions within a dataset

PGStats — Sun, 07 Oct 2018 02:35:35 GMT

What do you expect about the relation between Y and X1 for different stocks? Do you expect them to have a common slope but different intercepts? As in Y = B0s + B1*X1, where the B0s are a stock-specific intercepts. This kind of relationship can (and should) be fitted with a single regression.

Re: Multiple linear regressions within a dataset

PaigeMiller — Sun, 07 Oct 2018 11:02:19 GMT

@PGStats wrote:

What do you expect about the relation between Y and X1 for different stocks? Do you expect them to have a common slope but different intercepts? As in Y = B0s + B1*X1, where the B0s are a stock-specific intercepts. This kind of relationship can (and should) be fitted with a single regression.

Excellent point!

Re: Multiple linear regressions within a dataset

svw1900 — Sun, 07 Oct 2018 22:28:27 GMT

Ok Maybe I'm completely wrong with what I thought.

So what I Need is the correlation between y_var and all the x_variables in General. In a normal Regression, you would therefore compare all the data from all columns an receive the correlation, intercepts, parameters for x_variables etc. In my case, however, a normal regression at the level of the overall dataset would not make sense because the y_variable is Clustered in subgroups (the stocks), right? That's Why I thought I need multiple regressions, one for every Stock and its time-series.

Because of that I thought that the Output would be a set of Regression results, one for each subgroup. But that would not be what I Need at the end, since I need a general Information about the correlation between y and all the x's. Something like an aggregated correlation over all subgroups.

Maybe I am completely wrong in any of these points, in this Case Thanks for clarification.

Kind regards

Re: Multiple linear regressions within a dataset

PaigeMiller — Sun, 07 Oct 2018 23:41:17 GMT

@svw1900 wrote:
Ok Maybe I'm completely wrong with what I thought.

So what I Need is the correlation between y_var and all the x_variables in General. In a normal Regression, you would therefore compare all the data from all columns an receive the correlation, intercepts, parameters for x_variables etc. In my case, however, a normal regression at the level of the overall dataset would not make sense because the y_variable is Clustered in subgroups (the stocks), right? That's Why I thought I need multiple regressions, one for every Stock and its time-series.

Because of that I thought that the Output would be a set of Regression results, one for each subgroup. But that would not be what I Need at the end, since I need a general Information about the correlation between y and all the x's. Something like an aggregated correlation over all subgroups.

Maybe I am completely wrong in any of these points, in this Case Thanks for clarification.

Kind regards

Do you agree with @PGStats that you want different intercepts for each stock, but common slope??? Or do you want different slopes for each stock?

You also now are speaking clearly about multiple X variables, which was absent from your original example which contained only a single X variable. Which would then translate to different intercepts for each stock, but common slopes (plural) for each X. Is that what you want?

Re: Multiple linear regressions within a dataset

svw1900 — Mon, 08 Oct 2018 04:13:14 GMT

Sorry, seems like I Needed some Moments to understand the point Here. Yeah, I only expect different intercepts so a single Regression will probably fit for this case, you're right. Sorry for the confusion!

Re: Multiple linear regressions within a dataset

PaigeMiller — Mon, 08 Oct 2018 11:47:13 GMT

proc glm data=have;
    class stock_identifier;
    /* add as many X variables as you need here */ 
    model y = stock_identifier x1 x2 x3 /noint;
run;
quit;

Re: Multiple linear regressions within a dataset

Rick_SAS — Mon, 08 Oct 2018 23:09:58 GMT

Follow PaigeMiller's advice, but also use the TABLEOUT OUTEST= option on the PROC REG statement:

proc reg data=have TABLEOUT outest=RegOut;

...

quit;

The dataset RegOut contains the parameter estimates, standard errors, p-values, and 95% CIs. Here is an example:

proc sort data=sashelp.class out=Have;
    by sex;
run;
proc reg data=have outest=RegOut TABLEOUT plots=none;
    by sex;
    model height = weight;
run;
quit;

proc print data=RegOut;
var Sex _TYPE_ Intercept Weight;
run;

/* to output only some statistics, use a WHERE clause */
proc print data=RegOut;
where _TYPE_="PARMS";
var Sex _TYPE_ Intercept Weight;
run;