Regression Coefficient Help

husky

New Member
#1
Hello,

Thanks in advance for the help everyone, I'm new to this site and I really appreciate it.

I am currently working on some research and have begun to evaluate my results. I have several multiple regressions and need help discussing the regression coefficients. The difficulty I am having is that the two independent variables are different units (and I'm somewhat new to analyzing regressions). One is in dollars (x1 - e.g. $5.20) and the other is percent (x2 - e.g. 5.2%). The dependent variable is also in percent. If I come up with a regression output of Y= 0.068X1 + 1.115x2 + b what effects on my dependent variable do each of these independent variables have for each unit increase in the independent variable? So if I increase X1 by one unit, is the average increase in Y 6.8% or .068% or neither? And does a one unit increase in X1 mean one cent or one dollar? Same question with x2 which is a percentage.

Thank you so much for the help, I look forward to seeing what you have to say!
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
For clarification, you are conducting linear regression, correct? What program are you using, I ask because you should also be able to submit estimate states, where you can play around with the values of X1 and X2 and see the effects on generated Ys.

To my understanding, a 1 unit increase in X1 should result in a 0.068 increase in Y, but we may need more information from you to better interpret. In particular, how are your Ys formatted, (e.g., 36% or 0.36, with our without the leading zero and decimal)? Also, can you provide a little more detail on the context and what these variables represent - this helps put interpretations into understandable words and whether they make practical sense.
 

husky

New Member
#3
For clarification, you are conducting linear regression, correct? What program are you using, I ask because you should also be able to submit estimate states, where you can play around with the values of X1 and X2 and see the effects on generated Ys.

To my understanding, a 1 unit increase in X1 should result in a 0.068 increase in Y, but we may need more information from you to better interpret. In particular, how are your Ys formatted, (e.g., 36% or 0.36, with our without the leading zero and decimal)? Also, can you provide a little more detail on the context and what these variables represent - this helps put interpretations into understandable words and whether they make practical sense.
Thanks for the response!

I am conducting a linear regression. I am actually just using the data analysis tool in excel to conduct my regressions.

The variables:
Y: Percentage change in stock price - Formatted in % (e.g. 25%)
X1: Change in operating metric per share - formatted in $ (e.g. $5)
X2: change in market price - Formatted in % (e.g. 20%)

Thanks again
 

hlsmith

Less is more. Stay pure. Stay poor.
#4
My interpretation would be a mean 0.068 increase in the Y (percent without leading zero). This interpretation makes some sense when seeing X2 increases Y by a whole percent meaning X1 is only increasing by a partial percent per unit X1 increase and I would also expect the p-value to be fairly large with X1 since it has such a small beta coefficient. However this latter statement may not always be true if the variable(X1) had an infinitesimally small standard error, it could definitely be a significant predictor.
 

husky

New Member
#5
Thanks for that interpretation.

Is the change in one unit of X1, a change of $0.01 or a change of $1.00? A change of $1.00 would be pretty insignificant while $0.01 would be quite significant. Out of the 9 I ran (different forms of x1), two provided strong t-stats (above 2) and near zero p-values. So in those terms the results were good.
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
How is X1 getting entered in? You state "X1: Change in operating metric per share - formatted in $ (e.g. $5)"

Does that mean you are only entering whole numbers in for X1 within the model?
 

husky

New Member
#9
No, I'm sorry, I thought by whole numbers you meant not percentages. All the numbers went out two decimal points. Sorry about that. Would that change it to $0.01 increases?
 

hlsmith

Less is more. Stay pure. Stay poor.
#10
I found this example in Excel that may help you understand this.

panko.shidler.hawaii.edu/Courses/310/Handoutfor12&13.doc
 

hlsmith

Less is more. Stay pure. Stay poor.
#11
From my understanding of this on page 5, sq footage went in as a decimal, beta coefficient was 1.6699, representing a 1.67 change per 1 sq foot.

Given this example, a dollar increase should change your Y by 0.068.