how to calculate simple linear regression equation

Following are formulas for estimating sample sizes when focused on estimating the slope or the intercept. Earlier in this chapter we provided a sample size formula for correlation. The correlation is the best metric of overall quality, but depending on the situation, you might be more focused on the slope or the intercept. The first step in determining a sample size for linear regression is to decide which aspect is of primary interest. Sample size estimation for linear regression In other words, Usability appeared to be more than three times as important as Stability in predicting customer loyalty. In this model, Stability had a standardized weight of 0.188 and the standardized weight for Usability was 0.641. The standardization process converts each raw coefficient into a standard score, making their values comparable. Multiple regression also provides a way to compare the importance of the different independent variables (predictors) by examining their standardized coefficients. Alone, Stability accounted for 24% of the variability in LTR, but after adding Usability the regression model explained 56%. Adding usability to the model, the resulting equation was LTR = −0.937 + 0.541(Stability) + 0.419(Usability), with an R 2 of 56%. For the independent variable of Stability, the regression equation was LTR = 1.950 + 1.423(Stability), with a correlation of 0.49 and corresponding R 2 of 24%. I then used regression to evaluate the extent to which these variables predicted LTR. They also rated the stability of the system (whether it crashed) and its usability (using a four-item questionnaire).

I once had 2584 customers rate their likelihood to recommend (LTR) a university’s learning management system (LTR is a common measure of customer loyalty). The computational methods of multiple regression are similar to those of simple linear regression, but if you need to evaluate more than one independent variable, we recommend using a statistical program designed for these types of analyses (e.g., SPSS, SAS, R, Minitab).

How to calculate simple linear regression equation