Housing price is influenced by natural, social, economic and other factors. Only by understanding and conducting specific research on these influencing factors can people grasp the laws of housing price movements. Focusing on this issue, this paper chooses the average unit housing prices and their influencing factors of 11 cities in Zhejiang Province in 2022 as the research objects, then establishes a model reflecting the quantitative relationship between housing price and influencing factors. Firstly, relevant data is collected from official websites, including housing prices and 10 main influencing factor indicators of above cities. Secondly, principal component analysis is used for data preprocessing, and five prominent indicators are selected by calculating the relative contribution rate of each factor. Then, by drawing functional images and solving correlation coefficients, a qualitative analysis is conducted on the basic algebraic structure of the regression model. The results indicate that all independent variables include independent terms and cross-terms. Subsequently, through polynomial regression, data matrices for both dependent variable and independent variables are set to solve the coefficients of constant term, linear terms, quadratic independent terms and quadratic cross-terms respectively. Therefore, a model of factors influencing housing price is established. Finally, residuals sum of squares, mean square error, regression sum of squares and determination coefficient are calculated in sequence for the regression model. It turns out that all the statistics are within the ideal range, indicating high precision of data fitting and verifying the accuracy and reliability of the model.