ABSTRACT
A widely heard convention for sample size in regression is that a researcher needs at least 10 cases for every independent variable in the model. In the case of simple linear regression, that would suggest a sample size of 10 provides sufficient power. The regression estimates are quite sensitive to outlying observations such that the precision of the estimates is affected, particularly the slope. Also, the coefficient of determination can be affected. In general, the regression line will be pulled toward the outlier, because the least squares principle always attempts to find the line that best fits all of the points. The most commonly used transformations to correct for nonnormality in regression analysis are to transform the dependent variable using the log or the square root. The regression model and its parameter estimates are valid only for those values of X actually sampled.
