R - 季节性时间序列的线性回归 model

Question

I'm working with monthly averages. I have data for 24 years. (so 12 * 24 = 288 rows). I'm trying to create linear regression model using function tslm (viz. code).

library(tidyverse)
library("tseries")
library(forecast)

data <- read_csv("data.csv")

data$START_TIME <- as.Date(data$START_TIME)

data_TS <- ts(data$VALUE, frequency = 12)

fit <- tslm(data_TS ~ trend + season)

summary(fit)

Currently the output is:

Residuals:
     Min       1Q   Median       3Q      Max 
-19.9684  -4.6493  -0.0578   3.9262  23.3977 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  70.803362   1.628675  43.473  < 2e-16 ***
trend        -0.009475   0.005170  -1.833  0.06794 .  
season2      11.006465   2.066983   5.325 2.13e-07 ***
season3      11.540922   2.067002   5.583 5.76e-08 ***
season4      13.159978   2.067034   6.367 8.31e-10 ***
season5      12.753431   2.067080   6.170 2.50e-09 ***
season6      11.666369   2.067138   5.644 4.22e-08 ***
season7      -6.322834   2.067209  -3.059  0.00245 ** 
season8     -24.284647   2.067293 -11.747  < 2e-16 ***
season9     -34.434003   2.067390 -16.656  < 2e-16 ***
season10    -35.778105   2.114752 -16.918  < 2e-16 ***
season11    -27.213367   2.089425 -13.024  < 2e-16 ***
season12    -14.267532   2.140674  -6.665 1.49e-10 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.16 on 269 degrees of freedom
  (4 observations deleted due to missingness)
Multiple R-squared:  0.8778,    Adjusted R-squared:  0.8723 
F-statistic:   161 on 12 and 269 DF,  p-value: < 2.2e-16

I want to create equation from the output, but I'm missing coefficient for season 1.

Can anyone please explain me how to interpret values in the summary and how to create equation of linear model of my data?

Thank you

Answer 1

The fit has an intercept. So, the intercept is showing you the value when season1 . Otherwise, there would be no meaning for the intercept. If you want it explicit, you can make your model show

fit <- tslm(data_TS ~ 0 + trend + season)

[edit more information per followup question]

One way to think about this is to try to imagine manually using the model to get the estimated value of data_TS - you can see that if you had an intercept and all 12 seasons, you would be able to get a value when none of the season factors were true. That value would be the intercept.

The tslm output is like other lm outputs. There are many guides to learning about them on the web. Most assume that you understand what a linear regression model is doing from statistics text. You might want to search for 'interpret linear model results in R'. Here's one result that has a bit of detail on each output item from Felipe Rego