# INTERPRET A REGRESSION MODEL WHEN OUTCOME VARIABLE IS LOG TRANSFORMED [duplicate]

I have used a linear model between a log-transformed outcome variable and a group of predictor variables. In this model, the dependent variable is in its log-transformed state, and the independent variable is in its original metric.

> summary(model_lm_final_2)

Call:
lm(formula = log(Inflow) ~ Film + Episodes_1_5 + Episodes_6_10 +
Episodes_11_15 + Season_1 + Season_2 + Season_3 + January +
February + March + April + May + June + July + September +
October + November + Friday + Dutch + English + Release_once +
Programma + Kinderserie + TV_series + Documentaire + Drama +
Komedie + Thriller + Actie + Animatie + Romantiek + Avontuur +
Kids + Minage0 + Minage6 + Minage9 + Indecent_language +
Same_year_release, data = inflow_data_tbl_2)

Residuals:
Min      1Q  Median      3Q     Max
-4.9426 -0.7192  0.0443  0.7461  4.0083

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)        3.99520    0.29083  13.737  < 2e-16 ***
Film              -1.40755    0.18163  -7.750 1.61e-14 ***
Comedy             0.61367    0.10873   5.644 1.96e-08 ***
Romantic           0.73790    0.16439   4.489 7.67e-06 ***
Avontuur           1.14559    0.30325   3.778 0.000164 ***
Same_year_release  0.82898    0.09068   9.142  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.177 on 1621 degrees of freedom
Multiple R-squared:  0.4881,    Adjusted R-squared:  0.4761
F-statistic: 40.68 on 38 and 1621 DF,  p-value: < 2.2e-16


I want to understand the signs of the coefficient and the interpretation which I am making as below is correct. I am a bit confused with some percentage increase for inflow for some features below.

Feature 1 :: Film
To interpret the amount of change in the original metric of the outcome, I know we first exponentiate the coefficient of census to obtain exp(-1.40755) =  0.2447422. To calculate the percent change, we can subtract one from this number and multiply by 100 i.e. (1 - 0.2447422) * 100.

Thus, for a one unit increase in the Film, the inflow (number of people joining in) decrease by 75 percent.

Feature 2 :: Comedy
To interpret the amount of change in the original metric of the outcome, I know we first exponentiate the coefficient of census to obtain exp(0.61367) =  1.847198. To calculate the percent change, we can subtract one from this number and multiply by 100 i.e. (1 - 1.847198) * 100.

Thus, for a one unit increase in the Comedy, the inflow (number of people joining in) increase by 84.72 percent.

Feature 3 :: Romantic
To interpret the amount of change in the original metric of the outcome, I know we first exponentiate the coefficient of census to obtain exp(0.73790) =  2.091539. To calculate the percent change, we can subtract one from this number and multiply by 100 i.e. (1 - 2.091539) * 100.

Thus, for a one unit increase in the Comedy, the inflow (number of people joining in) increase by 109.15 percent.

Feature 4 :: Avontuur
To interpret the amount of change in the original metric of the outcome, I know we first exponentiate the coefficient of census to obtain exp( 1.14559) =  3.144296. To calculate the percent change, we can subtract one from this number and multiply by 100 i.e. (1 -  3.144296) * 100.

Thus, for a one unit increase in the Comedy, the inflow (number of people joining in) increase by 214.42 percent.

Feature 4 :: Same_year_release
To interpret the amount of change in the original metric of the outcome, I know we first exponentiate the coefficient of census to obtain exp(0.82898 ) =  2.290981. To calculate the percent change, we can subtract one from this number and multiply by 100 i.e. (1 - 2.290981) * 100.

Thus, for a one unit increase in the Comedy, the inflow (number of people joining in) increase by 129.09 percent.

• Could someone please provide me insight regarding the calculation I am making?
• When I should use increase or decrease given the coefficient sign in the linear model?
• Also if my interpretation of the coefficients is correct giving percent increase in inflow?