Multiple linear regression (mlr) example:

fit <- lm(y ~ x1 + x2 + x3, data=mydata)

Download data used in this tutorial.

Load data:

df<- read.csv("D:\\R4Researchers\\LAI_factors.csv")
View(df)
head(df)

Rename some long names of columns:

library(tidyverse)
df<- df %>% 
  rename(
    lst = LST_India,
    temp = Mean_air_tem_India,
    precip = Total_precipitation_India,
    humid = Hum_India
  )
head(df)

MLR

fit1 <- lm(LAI_China ~ LST_China + Tem_China + Precipitation_China + Hum_China, data = df) #building model
fit2 <- lm(LAI_India ~ lst+ temp + precip + humid, data = df)

summary(fit1) # show results
coefficients(fit1) # model coefficients
confint(fit1, level=0.95) # CIs for model parameters
fitted(fit1) # predicted values
residuals(fit1) # residuals
anova(fit1) # anova table
vcov(fit1) # covariance matrix for model parameters
influence(fit1) # regression diagnostics

summary(fit2)
coefficients(fit2)
confint(fit2, level=0.95)
fitted(fit2)
residuals(fit2) 
anova(fit2) 
vcov(fit2) 
influence(fit2)

Diagnostic plots:

Checks for heteroscedasticity, normality, and influential observations

layout(matrix(c(1,2,3,4),2,2)) # optional 4 graphs/page
plot(fit1)

Remove not significant variables from model:

fit3 <- lm(LAI_India ~ lst+ temp , data = df)
coefficients(fit3)
#(Intercept)         lst        temp 
# 1.2433245  -0.1124670   0.1154845

Interpret the results

In our example, it can be seen that p-value of the F-statistic (fit2) is 0.004692, which is significant. This means that, at least, one of the predictor variables is significantly related to the outcome variable.

LAI in India is significantly associated with lst and air temperature. Decreasing one degree of lst and increasing air temperature leads to an increase of 0.12 unite in LAI.

Model accuracy assessment

We can use R2 and Residual Standard Error (RSE) in summary. An R2 value close to 1 displays that the model interprets a large portion of the variance in the outcome variable. While the RSE provides a measure of error of prediction.

Extracting R-squared

summary(fit3)$r.squared  
# 0.6575707
summary(fit3)$adj.r.squared
# 0.6048892

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