I would like to solve a log-linear equation and interpret the final result. I was noted that my question was not complete/unclear. Fine, now I took a dataset from Kaggle as the example to demo what is my question and what kind of answer I am looking for. This dataset is not the real one that I am dealing with. But I guess the Kaggle's dataset could explain well the same problem:
So if I want to predict Windspeed, I set windspeed as label and Temperature, Humidity, Wind bearing Degrees and Visibility as independent variables. All these variables are numerical data.The below is my result form R:
Call: lm(formula = log(WindSpeed) ~ Temp + Humidity + WindbearingDegrees + Visibility, data = data) Residuals: Min 1Q Median 3Q Max -3.3211 -0.3657 0.1000 0.4272 1.8679 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 4.193e+00 2.750e-02 152.48 <2e-16 *** Temp -1.466e-02 2.819e-04 -52.00 <2e-16 *** Humidity -1.141e+00 1.363e-02 -83.72 <2e-16 *** WindbearingDegrees 8.023e-04 1.897e-05 42.29 <2e-16 *** Visibility 9.359e-03 5.357e-04 17.47 <2e-16 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.6315 on 96448 degrees of freedom Multiple R-squared: 0.0923, Adjusted R-squared: 0.09226 F-statistic: 2452 on 4 and 96448 DF, p-value: < 2.2e-16
Please don't judge the result e.g. Adjusted R-squared values. This is just a demo. My formula of this problem is:
MY QUESTION-How to solve the equation if I want to "undo" the logarithm step? I know I need to apply the exponential function to the formula. But how? Can anyone show me a step by step calculation? I would highly appreciate if you could also give me an interpretation to the final result e.g. what happens if one independent variable increases by one unit, holding all the other variables fixed.... Thank you!
=====my original question=====
I have got this equation:
Now if I would like to take the log away from the left side, how should I calculate on the right side? Like this?
y=exp(3.17+1.05*X1-1.01*X2) =exp(3.17)exp(1.05)*X1/exp(1.01)*X2 =23.81*2.86*X1/2.75*X2
Also if you could give an interpretation based on result, that would be super help. Thank you!