Data_Dive_Week11_Ankit

1. Build a linear (or generalized linear) model as you like

• Use whatever response variable and explanatory variables you prefer

2. Use the tools from previous weeks to diagnose the model

• Highlight any issues with the model

3. Interpret at least one of the coefficients

# Read the dataset
weather_data <- read.csv("C:\\Users\\singh\\Documents\\StatsR\\dataset\\Final\\weather_repo.csv")
# Selecting predictor variables and handling missing values
predictors <- c("humidity", "wind_kph", "air_quality_PM2.5", "air_quality_PM10")
weather_data_cleaned <- na.omit(weather_data[, c("temperature_celsius", predictors)])
head(weather_data_cleaned)

##   temperature_celsius humidity wind_kph air_quality_PM2.5 air_quality_PM10
## 1                28.8       19     11.5               7.9             11.1
## 2                21.3       54      3.6              31.7             39.3
## 3                18.1       40      3.6               7.7             12.8
## 4                19.2       49      3.6              20.9             52.4
## 5                18.5       40      3.6              10.8             24.3
## 6                17.0       27      3.6              12.2             25.9

Linear Model Building

We build a linear model with temperature in Celsius as the response variable and humidity, wind speed, and air quality indices as explanatory variables.

# Selecting variables
response_var <- weather_data_cleaned$temperature_celsius
explanatory_vars <- weather_data_cleaned[, c('humidity', 'wind_kph', 'air_quality_PM2.5', 'air_quality_PM10')]

# Building the linear model
model <- lm(temperature_celsius ~ humidity + wind_kph + air_quality_PM2.5 + air_quality_PM10, data = weather_data_cleaned)

summary(model)

## 
## Call:
## lm(formula = temperature_celsius ~ humidity + wind_kph + air_quality_PM2.5 + 
##     air_quality_PM10, data = weather_data_cleaned)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -19.298  -4.614   0.737   5.165  17.764 
## 
## Coefficients:
##                    Estimate Std. Error t value Pr(>|t|)    
## (Intercept)       25.053903   0.522208  47.977  < 2e-16 ***
## humidity          -0.059601   0.006151  -9.690  < 2e-16 ***
## wind_kph           0.136176   0.016840   8.086 9.43e-16 ***
## air_quality_PM2.5 -0.044661   0.006878  -6.493 1.01e-10 ***
## air_quality_PM10   0.039191   0.005165   7.587 4.56e-14 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.16 on 2529 degrees of freedom
## Multiple R-squared:  0.09699,    Adjusted R-squared:  0.09556 
## F-statistic: 67.91 on 4 and 2529 DF,  p-value: < 2.2e-16

Observations

• R-squared: The model explains about 9.6% of the variability in the temperature, which is relatively low, indicating that other unaccounted factors might also significantly influence temperature.
• Coefficients:
  • Humidity: For each unit increase in humidity, the temperature decreases by approximately 0.059 degrees Celsius.
  • Wind Speed (kph): For each km/h increase in wind speed, the temperature increases by approximately 0.136 degrees Celsius.
  • Air Quality PM2.5: For each unit increase in PM2.5, the temperature decreases by approximately 0.044 degrees Celsius.
  • Air Quality PM10: For each unit increase in PM10, the temperature increases by approximately 0.039 degrees Celsius.

Diagnostics of the Model

# Calculating MSE
predicted <- predict(model, weather_data_cleaned)
mse <- mean((weather_data_cleaned$temperature_celsius - predicted)^2)
print(paste("MSE:", mse))

## [1] "MSE: 37.8703498574756"

Interpretation

MSE of 37.87 suggests that on average, the model’s predictions deviate from the actual observed temperatures by the square root of 37.87, which is approximately 6.15 degrees Celsius.

Multicollinearity Check

We check for multicollinearity using Variance Inflation Factor (VIF)

# Checking for multicollinearity (VIF)
vif(model)

##          humidity          wind_kph air_quality_PM2.5  air_quality_PM10 
##          1.057367          1.021015          9.010306          9.038898

Multicollinearity: The Variance Inflation Factor (VIF) values for air quality PM2.5 and PM10 are relatively high (above 8), suggesting potential multicollinearity issues. This means these variables might not be providing independent information.

Coefficient Interpretation

Interpreting the coefficient of humidity.

coef(summary(model))["humidity", ]

##      Estimate    Std. Error       t value      Pr(>|t|) 
## -5.960139e-02  6.150547e-03 -9.690422e+00  7.895244e-22

Humidity: The negative coefficient for humidity (-0.0596) suggests that as humidity increases, the temperature tends to decrease, holding other factors constant. This could be due to the cooling effect of moisture in the air.