This paper proposes methodologies for statistical inference of low-dimensional parameters in high-dimensional linear models. The focus is on constructing confidence intervals for individual coefficients and linear combinations of several coefficients in a linear regression model. Theoretical results provide sufficient conditions for the asymptotic normality of the proposed estimators and consistent estimation of their finite-dimensional covariance matrices. These conditions allow the number of variables to far exceed the sample size. Simulation results demonstrate the accuracy of the coverage probability of the proposed confidence intervals, supporting the theoretical results. Key concepts include confidence intervals, p-values, statistical inference, linear regression models, and high-dimensional data. The paper discusses the challenges of statistical inference in high-dimensional data, particularly in the large-p-smaller-n setting. It highlights the importance of variable selection consistency and the limitations of existing methods in this context. The paper introduces a low-dimensional projection (LDP) approach to constructing confidence intervals without assuming the uniform signal strength condition. This approach allows for the construction of confidence intervals for preconceived regression coefficients or contrasts based on a small number of coefficients. The LDP method is also shown to be compatible with multiplicity adjustment, providing more information about unknown regression coefficients than variable selection. The paper presents a methodology for constructing confidence intervals for individual regression coefficients and their linear combinations in a linear model. It discusses the use of bias-corrected linear estimators and low-dimensional projections. Theoretical results justify the use of LDP confidence intervals for statistical inference, with the accuracy of the coverage probability supported by simulation results. The paper also discusses the use of the scaled Lasso and the least squares estimator in the model selected by the scaled Lasso (scaled Lasso-LSE) for consistent estimation of the noise level and initial estimator. The paper provides theoretical results for the asymptotic normality of the LDPE and the validity of the resulting confidence intervals. These results are supported by simulation experiments and theoretical analysis. The paper concludes that the LDP approach provides a more accurate and efficient method for statistical inference in high-dimensional linear models compared to existing variable selection approaches.This paper proposes methodologies for statistical inference of low-dimensional parameters in high-dimensional linear models. The focus is on constructing confidence intervals for individual coefficients and linear combinations of several coefficients in a linear regression model. Theoretical results provide sufficient conditions for the asymptotic normality of the proposed estimators and consistent estimation of their finite-dimensional covariance matrices. These conditions allow the number of variables to far exceed the sample size. Simulation results demonstrate the accuracy of the coverage probability of the proposed confidence intervals, supporting the theoretical results. Key concepts include confidence intervals, p-values, statistical inference, linear regression models, and high-dimensional data. The paper discusses the challenges of statistical inference in high-dimensional data, particularly in the large-p-smaller-n setting. It highlights the importance of variable selection consistency and the limitations of existing methods in this context. The paper introduces a low-dimensional projection (LDP) approach to constructing confidence intervals without assuming the uniform signal strength condition. This approach allows for the construction of confidence intervals for preconceived regression coefficients or contrasts based on a small number of coefficients. The LDP method is also shown to be compatible with multiplicity adjustment, providing more information about unknown regression coefficients than variable selection. The paper presents a methodology for constructing confidence intervals for individual regression coefficients and their linear combinations in a linear model. It discusses the use of bias-corrected linear estimators and low-dimensional projections. Theoretical results justify the use of LDP confidence intervals for statistical inference, with the accuracy of the coverage probability supported by simulation results. The paper also discusses the use of the scaled Lasso and the least squares estimator in the model selected by the scaled Lasso (scaled Lasso-LSE) for consistent estimation of the noise level and initial estimator. The paper provides theoretical results for the asymptotic normality of the LDPE and the validity of the resulting confidence intervals. These results are supported by simulation experiments and theoretical analysis. The paper concludes that the LDP approach provides a more accurate and efficient method for statistical inference in high-dimensional linear models compared to existing variable selection approaches.