Abstract Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets the data. Unfortunately, such fine-grained analysis can easily reveal individual information. We study regression algorithms that satisfy differential privacy , a constraint which guarantees an algorithm’s output reveals little a...

One of the most widely used statistical techniques is simple linear regression. This technique is used to relate a measured response variable, Y, to a single measured predictor (explanatory) variable, X, by means of a straight line. It uses the principle of least squares to come up with values of the “best” slope and intercept for a straight line that approximates the relationship. By means of ...

Rationale Frequently decision-making situations require modeling of relationships among business variables. For instance, the amount of sale of a product may be related to its advertising expenditures for marketing, the health of the economy as measured by the stock market performance, and the number of sales people etc? The regression analysis provides tools for modeling a "response" variable ...

In this tutorial article, the concepts of correlation and regression are reviewed and demonstrated. The authors review and compare two correlation coefficients, the Pearson correlation coefficient and the Spearman rho, for measuring linear and nonlinear relationships between two continuous variables. In the case of measuring the linear relationship between a predictor and an outcome variable, s...

Many people who do data analysis take only a few classes in statistics and hence, in general, get introduced only to classical methods of statistics; i.e., least squares, normal theory, and possibly maximum likelihood methods. The motivation for most of these techniques is the maximizing of a function of the data with respect to some parameter—mean, variance, slope, e.g. Calculus is used by tak...

We start with the simple case of studying the relationship between a response variable Y and a predictor variable X I . Since we have only one predictor variable, we shall drop the subscript in X I and use X for simplicity. We discuss covariance and correlation coefficient as measures of the direction and strength of the linear relationship between the two variables. Simple linear regression mo...