2nd degree polynomial regression: Model is not full rank

[littlewho]

Hello,

I am trying to run a 2nd degree regression on a dataset looking like the following:

	date	returns	continuous_date	continuous_dateSquared
1	2007Q4	-0.53	2007.75	4031060.0625

2

2008Q1

-5.11

2008

4032064

3

2008Q2

-3.176666667

2008.25

4033068.0625

4

2008Q3

-1.516666667

2008.5

4034072.25

5

2008Q4

-6.57

2008.75

4035076.5625

6

2009Q1

-8.495

2009

4036081

7

2009Q2

0.1066666667

2009.25

4037085.5625

8

2009Q3

6.475

2009.5

4038090.25

9

2009Q4

12.72

2009.75

4039095.0625

10

2010Q1

1.265

2010

4040100

11

2010Q2

-0.125

2010.25

4041105.0625

12

2010Q3

0.565

2010.5

4042110.25

13

2010Q4

2.495

2010.75

4043115.5625

The regression equation should be like the following: Returns(t) = a + b * time(t) + c * time(t)^2 and the code looks like this:

proc reg data=temp;
   model returns=continuous_date continuous_dateSquared;
   ods output ParameterEstimates=params;
run;

When I try to run this, I'm getting the following error:

That's strange, because using the regression option from sgplot, works just fine:

ods graphics / reset width=8in height=6in imagemap;
proc sgplot data=temp;
	reg x=continuous_date y=returns_avg / degree=2 nomarkers; 
	scatter x=continuous_date y=returns_avg; 
run;
ods graphics / reset;
title;

Could anyone point what I am doing wrong?

Thanks!

[ballardw]

Note that your SGPLOT does not include the squared date.

Also see the parameter for continuous_dateSquared of zero? Meaning that the parameter is not actually used:

y= ax**2 + bx + c is the same as y=bx+c when a=0.

Not that reg is the best tool but the magnitude of the values for your "dates" are pretty large compared to the values of returns and the squared version is doing about what I would expect because of the magnitude.

You might see something marginally more useful if subtract something like 2006 from "continuous_date" and then square that value (which will yield values more in the range of 1.5 to 100 instead of 4,000,000). So "continuous date" would interpret as "year from 2006" instead of the absolute year.

[littlewho]

---

@ballardw wrote:

Note that your SGPLOT does not include the squared date.

---

I included the option "degree=2" in the sgplot reg instruction, shouldn't be this the way of including the squared date?

Thanks for the suggestion, I will try to rescale the parameters and see what I would get.

[smantha]

I see the following warnings in the code that supports Ballard's hypotheses

---

@littlewho wrote:

Hello,

I am trying to run a 2nd degree regression on a dataset looking like the following:

	date	returns	continuous_date	continuous_dateSquared
1	2007Q4	-0.53	2007.75	4031060.0625

2

2008Q1

-5.11

2008

4032064

3

2008Q2

-3.176666667

2008.25

4033068.0625

4

2008Q3

-1.516666667

2008.5

4034072.25

5

2008Q4

-6.57

2008.75

4035076.5625

6

2009Q1

-8.495

2009

4036081

7

2009Q2

0.1066666667

2009.25

4037085.5625

8

2009Q3

6.475

2009.5

4038090.25

9

2009Q4

12.72

2009.75

4039095.0625

10

2010Q1

1.265

2010

4040100

11

2010Q2

-0.125

2010.25

4041105.0625

12

2010Q3

0.565

2010.5

4042110.25

13

2010Q4

2.495

2010.75

4043115.5625

The regression equation should be like the following: Returns(t) = a + b * time(t) + c * time(t)^2 and the code looks like this:

proc reg data=temp;
   model returns=continuous_date continuous_dateSquared;
   ods output ParameterEstimates=params;
run;

When I try to run this, I'm getting the following error:

That's strange, because using the regression option from sgplot, works just fine:

ods graphics / reset width=8in height=6in imagemap;
proc sgplot data=temp;
	reg x=continuous_date y=returns_avg / degree=2 nomarkers; 
	scatter x=continuous_date y=returns_avg; 
run;
ods graphics / reset;
title;

Could anyone point what I am doing wrong?

Thanks!

---

---

@littlewho wrote:

Hello,

I am trying to run a 2nd degree regression on a dataset looking like the following:

	date	returns	continuous_date	continuous_dateSquared
1	2007Q4	-0.53	2007.75	4031060.0625

2

2008Q1

-5.11

2008

4032064

3

2008Q2

-3.176666667

2008.25

4033068.0625

4

2008Q3

-1.516666667

2008.5

4034072.25

5

2008Q4

-6.57

2008.75

4035076.5625

6

2009Q1

-8.495

2009

4036081

7

2009Q2

0.1066666667

2009.25

4037085.5625

8

2009Q3

6.475

2009.5

4038090.25

9

2009Q4

12.72

2009.75

4039095.0625

10

2010Q1

1.265

2010

4040100

11

2010Q2

-0.125

2010.25

4041105.0625

12

2010Q3

0.565

2010.5

4042110.25

13

2010Q4

2.495

2010.75

4043115.5625

The regression equation should be like the following: Returns(t) = a + b * time(t) + c * time(t)^2 and the code looks like this:

proc reg data=temp;
   model returns=continuous_date continuous_dateSquared;
   ods output ParameterEstimates=params;
run;

When I try to run this, I'm getting the following error:

That's strange, because using the regression option from sgplot, works just fine:

ods graphics / reset width=8in height=6in imagemap;
proc sgplot data=temp;
	reg x=continuous_date y=returns_avg / degree=2 nomarkers; 
	scatter x=continuous_date y=returns_avg; 
run;
ods graphics / reset;
title;

Could anyone point what I am doing wrong?

Thanks!

---

WARNING: The range of variable cont_date is so small relative to its mean that there may be loss of accuracy in the computations.
You may need to rescale the variable to have a larger value of RANGE/abs(MEAN), for example, by using PROC STANDARD M=0;
WARNING: The range of variable cont_date_sq is so small relative to its mean that there may be loss of accuracy in the
computations. You may need to rescale the variable to have a larger value of RANGE/abs(MEAN), for example, by using PROC
STANDARD M=0;