If you convert the Y variable to the log scale, then the beta coefficient for X will give you the percentage change in Y for every unit increase in X.

Hi Stavroula,

I agree with Ariel, for logistic regression, the beta coefficient is the best term to report because it is easiest to explain.  Beta is derived by taking e^B.  For instance, a beta coefficient of 1.25 is a 25% increase for every unit increase in X.  This is especially true for a continuous independent variable.  I hope this helps in your situation.  If you have specific questions about your research topic please feel free to ask.

Kumar

Won't using log y on the y-axis against x on the x-axis mean you have logy = bx + e and so b is the estimated change in logy with change in x, not the change in y with x, even if this is linear? Is that what is being discussed, or did I miss something?

If you have y = a + bx + e, where e, by the way, is generally heteroscedastic, and can be factored into a random factor of the estimated residual, and a nonrandom factor based on the regression weight, then it would seem that if you want to know the change in y for every unit change in x, you would best use the estimated coefficient b. - Guess it depends, however, upon the specific problem for which you are solving.

Have you plotted points on a scatterplot to see if linear regression appears justified? Does theory of the subject matter support this? 

James, here are more specific examples and their interpretations, depending on whether Y or X is logged:

(1) Assume Y = 0.5X [neither Y or X is logged]

A one-unit change in X leads to a 0.5-unit change in Y

(2) Y = 0.5ln(X) [only X is logged]

A 100-percent change in X leads to a 0.5-unit change in Y

(3) Assume ln(Y) = 0.5X [only Y is logged]

A one-unit change in X leads to a 50-percent change in Y

Thank you all  for your answer.

In order to became more specific i give you my situation (linear regression analysis).

If i have this result : Y= 780 -30,3*Growth rate

As you wrote above for one unit change in x , y is=  -30,3units 

My question is if x change 3,5% which is the change in y? per cent?

in which mathematic way can i calculate this and with which Β, or beta?

Stavroula,

In your example you have not logged either X or Y, so you are not intuitively representing a % change. 

When the X variable is logged, the change in a logged variable is just the proportional change in the unlogged variable, that would mean that a one unit increase in X would result in % increase in Y, proportionally (thus, not on a log scale)...

I should have also added the case where both Y and X are logged. In that scenario, the coefficient provides the percent change in Y due to a 1% increase in X.

Dear Ariel, thank you again,

you wrote "In your example you have not logged either X or Y, so you are not intuitively representing a % change". ok ,

what do you mean lag?

eg. if one year i have 3,5% change in x, the next year 3% chanfe in x then can i calcuate the percentage change in Y. iN my example , 3,5% change in x means -1,06% change in Y ,IS THIS CORRECT OR NOT?

Hi Stavroula,

I wrote "logged" not lagged. What I meant was that in your example, both the X and Y variables are on their original scale - no transformation was made to either the X or Y or both variables. In that case (referring to my earlier example #1), the one unit change in X leads to a 0.5-unit change in Y.

If you take the natural log of the Y variable (as in my previous example #3) and regress that on X (on the original scale) then a one-unit change in X leads to a 50-percent change in Y.

As an example, let's run a regression in which we want to see how an automobile's weight impacts its gas mileage (with our assumption being that a heavier car will have poorer gas mileage). The regression formula is as follows:

Predicted mileage = intercept + coefficientwt * auto wt

and with real numbers:

21.834789 = 39.44028 + -.0060087*2930

So this equation says that an automobile that weighs 2930 lbs is predicted to get 21.83 miles/gallon. Or if we look at the coefficient for wt, we see that for every additional pound of auto weight, we expect a reduction of -.006 miles/gallon.

Now let's take the natural log of mileage = ln(mileage) and rerun the regression:

3.049694 = 3.878298 + -.0002828*2930

The outcome is now the natural log of mileage, and the equation now says that an automobile that weighs 2930 lbs is predicted to get 3.05 miles/gallon on the natural log scale. This is not very informative as written, however the coefficient for weight is informative! It says that for every pound increase in auto weight, we predict a .028% decrease in miles/gallon.

I hope this response was sufficiently informative for you. If not, I suggest that you consult an introductory statistics book.

Good luck

Ariel

Stavroula -

I found your question under linear regression, which would indicate that y is estimated as a + bx, if just one regressor, and so if a = 0 then b sounded like a slope I thought that you were looking for, but when a is not equal to zero, then the percent change of y with change in x is not a constant b-value. The additional change in y is bx, however. I'm not really clear regarding your question.

Looking at your question again, I see that under "Topics" you also have "logistic regression." Are you looking for a probability of binary event y given x? If so, I did a little Internet searching, and the attached link may be of some use to you.

I also see that you listed the topic "Local Regression Analysis." Would that be something like lowess? That sounds like a different topic.

"Bayesian Regression" involves much more.

You might want to give some more clarifying details about your application and the problem you need to solve.

Cheers - Jim

http://www.strath.ac.uk/aer/materials/5furtherquantitativeresearchdesignandanalysis/unit6/whatislogisticregression/

Looking at what you later wrote, you had this:

"Y= 780 -30,3*Growth rate"

and you asked if

"3,5% change in x means -1,06% change in Y"

Well, for your estimate of y that you called Y, but I'll call y* (as an estimate or prediction of y), to decrease by 1.06%, when x started at 30.3 and then increased by 3.5%, with b=growth rate, this means that you have

y* = 780 - 30.3b

and simultaneously

0.9894y* = 780 - (30.3)(1.035)b

"Subtracting" the second equation from the first, so-to-speak, we get

0.0106y* = 0.035b

So when y is about 3.3 times b, that is the case where you found

"3,5% change in x means -1,06% change in Y"

However, when y is not near 3.3b, that will not be the case.

Does this address your question?

Thank you again for your answers and your time.They were helpfull, in order to unserstand better my case. I decided to calculate with coefficient B and take my result :

The percentage of influence on y ,because of change of x

S.B.

 Piyush,

I actually provided answers to this in my previous posts to this query. See my earlier posts and then ask again after reviewing them, if it is still not clear.

Ariel

Piyush,

If you use a logit model, why would you log Y? That doesn't make sense given that the outcome will be binary (unless you have a fractional model, but then I would use a GLM instead).

I also am not clear on what you are asking about x4 and x5? Are you interested in the odds ratio for these variables, or log odds? Your statistics package will give you these values depending on whether you specify the odds ratio or log odds option (in Stata you could use logit or logistic, or you could specify logit Y X, or).I am attaching a link to the UCLA website that provides a great short description of the logit model and its interpretation.Ariel

http://www.ats.ucla.edu/stat/stata/dae/logit.htm

Is there a compelling reason to transform x5 and x6 to begin with? I would check the relationship between Y and x's to see if you indeed need to transform them. I am not sure the value in running the model with these transformed, only to un-transform them for interpretation. The relationships will change between the various variables.

how we get pertentage of coefficient in two regimes

coef sd coef sd coef sd

income -7.10e 5.920 2.080 8.86e 2.18e 1.26e

this one variable in two regimes how we can take percentage and explain difference in each other.

Dear Ariel Linden and Friends,

I have read all your answers above ! Thank you so much !

Referring to :

Assume ln(Y) = 0.5X [only Y is logged]

A one-unit change in X leads to a 50-percent change in Y

So, If I have standardized my IVs (X) , then can I interpret as:

Assume ln(Y) = 0.5* standardized X [only Y is logged]

A one-std. deviation(say Std. dev it is 4.5 units) change in X leads to a 50-percent change in Y

Then, can I say :

4.5 units change leads to a 50% change in Y,

hence a 1 unit change will lead to a (50% divided by 4.5) % change in Y

- Is this answer correct ?

Regards

Sherin

Help, please!!!

My dependent variable is count dependent like in percentage (10%, 25%, 35%, 75% and 85% ---5 categories strictly). So I used GLM specifying family (negative binomial) and link (log) to analyze the data. Would you please guide me on the correct way of interpretation of the effect of independent variables on dependent variables for example a significant coefficient of 0.65 of particular predictor variable X on the response variable Y. It would be great if you suggest any similar research article. Thank you!!!

Sudip Adhikari