The Commerce Department also has data available on number of shopping
centers and retail sales for the South Centeral states.  The data are
given below:

State         #of Shopping Ctrs                 Retail Sales
($billion)
Kentucky            593                                11.7
Tennessee          1137                                19.1
Alabama             601                                13.2
Mississippi         418                                 7.2
Arkansas            339                                 6.4
Louisiana           676                                15.4
Oklahoma            556                                11.4   
Texas              2824                                72.7
Source: Statistical Abstract of the United States 1995.
a] find the linear regression model for the South Central states.
b]How does the equation for the South Central states compare to the
one you found for the North Central states?
c]fombine the data form the North Central and South Central sates and
find the linear regression model forthe combined data?

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Request for Question Clarification by calebu2-ga on 30 Jul 2002 07:43 PDT

Whosher,

You haven't provided the data for the north central states. So I can't
answer parts B and C of the question. If you copy those from the
textbook / homework sheet, I might be able to do the whole question.

Anyway in the mean time, here's how I did the first part :

Copied your text into microsoft excel.

Used the text to columns option under the Data menu to split it so
that the state was in column a, # of shopping centers in B, retail
sales in C. Data started on line 2.

I then went to Tools, Data Analysis and selected Regression (like the
question asked).

My input Y range (what you are trying to predict - Retail sales) :
C1:C8
My input X range (What you believe explains sales - # of centers) :
B1:B8

My output range : A10

I then clicked on OK and got the following results :

SUMMARY OUTPUT								
								
Regression Statistics								
Multiple R	0.99108938							
R Square	0.98225816							
Adjusted R Square	0.979301186							
Standard Error	3.140820786							
Observations	8							
								
ANOVA								
	df	SS	MS	F	Significance F			
Regression	1	3276.910219	3276.910219	332.1836325	1.75694E-06			
Residual	6	59.18853125	9.864755209					
Total	7	3336.09875						
								
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower
95.0%	Upper 95.0%
Intercept	-4.051231328	1.709499613	-2.369834598	0.055533231	-8.23422925	0.131766594	-8.23422925	0.131766594
X Variable 1	0.026527135	0.001455463	18.22590553	1.75694E-06	0.022965742	0.030088527	0.022965742	0.030088527
								
I can interpret these results as follows:

Intercept coefficient is -4.05123
x coefficient is 0.026527

So the model for sales is :

Sales = -4.05123 + 0.026527 * #ofCenters

If you want to understand a little bit about the math behind what I
just did (Well advised if this is for a statistics course - you will
typically be thrown a curve ball on the final to check whether you
understand the material - being able to quote the correct number will
not help you much), you could check out the following links :

Least Squares Fitting from Mathworld (Gives a background into the
mathematics of the least squares)
http://mathworld.wolfram.com/LeastSquaresFitting.html

Lesson in Linear Regression and Best fit from UIUC (provides a simple
to follow expose of the linear regression) :
http://www.mste.uiuc.edu/patel/amar430/intro.html

Search method used: "linear regression"

Anyway, if you want to post the rest of the data I will have a go at
working through the rest of the question, although I strongly suggest
that you follow the above steps to try and answer the question -
perhaps you can post your results here for clarification if you are
unsure that they are correct.

Let me know if you have any further questions.

calebu2-ga

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Request for Question Clarification by secret901-ga on 30 Jul 2002 08:19 PDT

The information need to to solve this problem can be found in any
elementary statistics book.  Homework can be boring, but they do help
you in the future.

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Clarification of Question by whosher-ga on 31 Jul 2002 07:29 PDT

Enclose you will find the North Central States info for Retail Sales -1994

State                Number of Shopping ctrs           Retail Sales ($billion)

Ohio                       1559                            34.8
Indiana                     848                            18.0
Illinois                   1961                            34.1
Michigan                    967                            21.0
Wisconsin                   588                            12.0
Minnesota                   436                            11.5
Iowa                        277                             6.3
Missouri                    834                            18.9
North Dakota                 84                             1.8
South Dakota                 51                             1.1
Nebraska                    245                             4.8
Kansas                      458                             9.7

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Request for Question Clarification by calebu2-ga on 02 Aug 2002 07:56 PDT

whosher,

See my comments on question:

https://answers.google.com/answers/main?cmd=threadview&id=46840

If you want I can create a similar question that tackles the issued
raised by this question and give you a somewhat detailed solution that
explains the background, the excel methodology and how to interpret
the answers. Let me know if this would be acceptable to you.

I cannot answer a whole textbook question verbatim without permission
from the author to do so.

Regards

calebu2

I'm curious:  how do we know that it makes sense to give the
regression and anova statistics to 8 significant digits when the input
data has three significant digits?

I guess though maybe this is accounted for in the uncertainty of the
regression parameters?

I know, it doesn't make sense. The standard errors, model errors and
data rounding errors will kick in far before the 8th digit. However,
if you are going to use the results in follow on work, it makes sense
to keep as many digits as possible to avoid a fourth type of error -
user carelessness.

For example - I saw students once calculate the average of three
numbers, 7, 10 and 13 by dividing each by three and then summing.
Unfortunately instead of getting 10 as their answer, they rounded
2.3333 to 2.3, 3.3333 to 3.3 and 4.3333 to 4.3. They got 9.9 as their
answer. That kind of rounding is just as ridiculous as not rounding at
all.

So, I just leave the numbers as is and let the person who is using the
results figure out their importance (interpretation of statistics is
far more important than the ability to produce them - listen to any
baseball fan and you'll see what I mean).

Anyway, precision isn't normally taken into consideration with a
regression analysis - the results given are based on an exact formula
that assumes the input is correct. If you knew the margin of error in
your inputs, you could back out the additional uncertainty in the
model but most people don't distinguish that from the statistical
uncertainty captured in the traditional regression output.