Introduction

This project is mainly to the linear effect temperature and air pressure on the precipitation of rain, snow and hail in Sweden. The locations of the weather stations in this study include Lund, Uppsala, and Abisko. The observation recorded monthly from 1945 to 2019. Some of the missing or incomplete data is deleted in this study in the given dataset (weatther.rda).

Visualization of Raw Data

Modeling Setting

Model Results

Diagnostic Check

LinearModel.1

  • Normal QQplot indicates that the rain variable follows fat-tail distribution and violates the normal distribution assumption in the linear regression model.
  • The residual against the fitted value indicates that the residual variance is too large. It implies that temperature is insufficient to explain the response of rain precipitation. There may be missing other explanatory variables.
  • It is not a good linear regression model.

LinearModel.2

  • log-lin transformation of LinearModel.2 is better than LinearModel.1
  • Because LinearModel.2 shows no system patten in residual plots whereas LinearModel.1 show obivious system pattern in residual plos.

The Best Model: LinearModel.2

Antilog(Best Model)

95% Confidence Intervals

One Degree Celsiuse Effect

Antilog(LinearModel.02) Vs LinearModel.01

Predict Rain Precipitation

Apprendix A