# Thread: Formula For Logarithmic Regression

1. ## Formula For Logarithmic Regression

Hello, I am aware the final formula is y=a+blnx, however I don't know the formulas to find a and b. I searched around everywhere and all I can find is how to do it on a calculator. Once this is found, how can I find the coefficient of determination as well? Thank you

2. Do you know how to do a normal linear regression? Do you know how to find the coefficient of determination (i.e., $R^2$) for a normal linear regression? If so, then think of this logarithmic transformation on X as just a standard X variable. In other words, let $X^*=ln(X)$, and do the normal stuff for the linear regression:

$Y = a + bX^*$

The transformation doesn't change the methodology of a regression, only the interpretation of the results.

3. Originally Posted by bryangoodrich
Do you know how to do a normal linear regression? Do you know how to find the coefficient of determination (i.e., $R^2$) for a normal linear regression? If so, then think of this logarithmic transformation on X as just a standard X variable. In other words, let $X^*=ln(X)$, and do the normal stuff for the linear regression:

$Y = a + bX^*$

The transformation doesn't change the methodology of a regression, only the interpretation of the results.
Thank you. However I am still getting a wrong result. Here is the dataset,

Y=
Code:
      1043       1148       1105       1218       1037       841       903       866       928       881       802       828       726
X=
Code:
      1       2       3       4       5       6       7       8       9       10       11       12       13
For the linear regression I get -32.5x+1176 which is consistent with Excel. However when I get the log of all of the X values and perform the normal linear regression as you say I get 237.9ln(x)+637.6 when the correct answer according to Excel is -148ln(x)+1204.9. I am not sure what I am doing wrong. I should be using the natural log of x throughout all of the summation calculations that require x correct? Thank you

4. You might want to check your calculations. I checked this in R and got the same results as Excel. See the code below. Results have been commented out.

Code:
y <- c(1043, 1148, 1105, 1218, 1037, 841, 903, 866, 928, 881, 802, 828, 726)
x <- 1:13
lnx <- log(x)
(fit <- lm(y ~ x))           ## y = 1176 - 32.52*x

#Call:
#lm(formula = y ~ x)

#Coefficients:
#(Intercept)            x
#    1175.77       -32.52

(fit.log <- lm(y ~ lnx))     ## y = 1205 - 148*log(x)

#Call:
#lm(formula = y ~ lnx)

#Coefficients:
#(Intercept)          lnx
#       1205         -148

5. Got it, thanks. The problem was my data-typing in my program, it was rounding the logged values.