Simple Linear Regresson of Building Dynamics

library(tidyverse)
library(magrittr)
options(tibble.width = Inf)

ti <- read_csv("~/GitHub/MatrixTSA/data/soenderborg_2day.csv")

ti_winter <- filter(
  ti,
  as.POSIXlt("2011-06-01")$yday < as.POSIXlt(ti$t)$yday &
  as.POSIXlt(ti$t)$yday <= as.POSIXlt("2011-10-01")$yday
  )
ti_winter

Get the data from house 3 during the winter in year 2011.

lm_winter_3 <- lm(P3 ~ Te, ti_winter)
summary(lm_winter_3)

Call:
lm(formula = P3 ~ Te, data = ti_winter)

Residuals:
    Min      1Q  Median      3Q     Max 
-203.19 -110.55  -44.61   64.59  643.97 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1166.733    118.136   9.876 1.06e-13 ***
Te           -53.936      7.419  -7.270 1.50e-09 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 165.3 on 54 degrees of freedom
  (5 observations deleted due to missingness)
Multiple R-squared:  0.4946,    Adjusted R-squared:  0.4852 
F-statistic: 52.85 on 1 and 54 DF,  p-value: 1.503e-09

par(mfrow = c(2, 2))
plot(lm_winter_3)

The P-values of coefficients for intercept and Te are sufficiently small, so it’s a good model. However, from the top-left diagram, we can say the residuals are not iid.

lm_3 <- lm(P3 ~ Te, ti)
summary(lm_3)

Call:
lm(formula = P3 ~ Te, data = ti)

Residuals:
   Min     1Q Median     3Q    Max 
-930.1 -342.0  -31.5  249.1 1611.2 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  3624.50      53.65   67.56   <2e-16 ***
Te           -210.26       4.82  -43.62   <2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 452.5 on 141 degrees of freedom
  (9 observations deleted due to missingness)
Multiple R-squared:  0.931, Adjusted R-squared:  0.9305 
F-statistic:  1903 on 1 and 141 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(lm_3)

When including the entire period, the span of the data is extended. There are more large residuals.

par(mfrow = c(1, 1))
acf(
  lm_winter_3$residuals, 
  main = "ACF of Residuals from Linear Reg Model `lm_winter_3`"
  )

acf(
  lm_3$residuals,
  main = "ACF of Residuals from Linear Reg Model `lm_3`"
  )

The residuals from lm_winter_3 are more correlated with each other than those from lm_3. The heating loads in summer may cause the difference.