For California housing prices data, housing median age as a potential confounding variable may affect the relationship between other covariates and response variable. If we ignore the effect of measurement errors on the variables and directly apply the classic semiparametric models assuming that the response variable and covariates can be accurately observed to fit the data, it may cause deviations in the results obtained. Therefore, we use singleindex distortion measurement errors model to fit these data. After observing the fitted curve of the distortion function, we find that the confounding variable housing median age has a connection with the median house value, median income, total rooms, total bedrooms and population. This shows that the singleindex distortion measurement errors model we choose is more suitable for California housing data than the semiparametric models that do not consider measurement errors.