Research On The Correlation Between Real GDP Per Capita And Other Economical Factors Of The Provincial Administrative Regions In China

It is regression analysis that is one of the fundamental techniques in statistics. R programming language is the implementation of all the statistical computing over the paper. We choose 11 common economic variables firstly to get the relations between real GDP per capita and these variables. Then we use multivariable analysis methods (principal component analysis) to do basic explorationary data analysis, by which we find that 99% of the variance can be illustrated with 3 principal components only, so it is necessary to select variables. In model selection, we use stepwise regression, which is the general technique in stepwise regression methods, using AIC, to select 5 variables out of the model, which can be research further. Then, we do residual analysis, and compare the QQ-plots of the model, and we recognize that there are unequal variances for the variables; either responses or the predictor should be transformed or adapted with weighted least squares. Here we use the Box-Cox transformation to make a power transformation for the predictor. The new model is not perfect, because there are 2 of 5 signs of the responses is opposite to economic principles; we combine this conflict and the result of multivariable analysis to get a conclusion that there are multicollinearity in the model. At the same time, we calculate the VIFs, and find that there are 2 VIFs of the regressors which are greater than 10. After this, ridge regression is used to reduce the power of multicollinearity; ridge regression choose a biased estimator, but with a smaller variance than those unbiased. We find out the best biased coefficient and get a final and reasonable model whose variables are fit the economic principles. At last we make a conclusion that real GDP per capita have positive relations with 4 economical factors and have negative relations with 1 economical factor.