Multiple linear regression (mlr) example:
fit <- lm(y ~ x1 + x2 + x3, data=mydata)
Download data used in this tutorial.
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)
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)
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.
summary(fit3)$r.squared # 0.6575707 summary(fit3)$adj.r.squared # 0.6048892
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