# 12- Multiple linear regression in R programming

Published on Jul 20, 2021

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Multiple linear regression (mlr) example:

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

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

#### 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)
`````` #### Interpret the results

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.

#### 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
``````

#### Model accuracy assessment

We can use R2 and Residual Standard Error (RSE). 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.

``````rmse <- sigma(fit3)/mean(df\$LAI_India)
rmse
# 0.02880172
``````

#### Extracting R-squared

``````summary(fit3)\$r.squared
# 0.6575707