Statistics for Research - L24 || #Regression Analysis using #R

Linear regression is presented as a practical way to predict a dependent outcome from one or more predictors, using a least-squares line that summarizes the pattern in data. After scatter plots and correlation analysis have already described direction, form, and strength of linear relationships, regression turns that relationship into a usable prediction tool: it estimates the dependent variable’s value based on independent variables, and it does so by choosing the line that stays as close as possible to the observed data points. The closer the line is to the points, the better the predictions—meaning the predicted y values land near the actual y values.

The lesson anchors the method with real-world examples: predicting house prices from size, bedrooms, and location; forecasting sales revenue from marketing spend, competitor activity, and economic indicators (using historical data from prior years); estimating probability of default from borrower characteristics like credit score, annual income, and debt-to-income ratio; and predicting student satisfaction from survey scores tied to university responsibility, service quality, and leadership. In each case, regression is framed as a bridge from observed relationships to forecasting outcomes.

A concrete walkthrough uses a scatter plot of “vision” versus “organizational performance.” As vision scores rise, organizational performance tends to increase, and the fitted line reflects that upward trend. To make a prediction, the process is illustrated by selecting an x value (vision score of 6), moving vertically to the regression line, and reading the corresponding y value (predicted organizational performance). The quality of the model is tied to how tightly most data points cluster around the line; when points sit near the line across the range of x values, the predictor is treated as useful.

The implementation in R follows a clear workflow. First, the stats package is loaded (it’s part of R’s base installation). Next, data are read from a CSV file in the same folder as the R script, with comma-separated values, and stored in an object (named data s in the transcript). The linear model is then fit using the lm() function, specifying the dependent variable (op) and the independent variable (vision) with the formula structure lm(op ~ vision, data = data s). Model results are extracted with summary(model), which returns residuals and key statistics.

Interpretation centers on whether vision has a significant impact on organizational performance. Significance is assessed using the t value and p value: the transcript notes significance when the t value exceeds 1.96 and the p value is below 0.01, with “three stars” indicating very small p-values. Model fit is summarized with R square, described as the percentage of variation in the dependent variable explained by the predictors (the example given is 38.34%). The F statistics and its p value provide an overall test of the model’s explanatory power.

Finally, the lesson extends to multiple regression. With more than one independent variable, the lm() formula uses plus signs (e.g., op ~ TAA + vision), and the same summary-based approach is used to retrieve coefficients, R square/adjusted R square, and F statistics. The transcript also mentions exporting results to Excel and using packages like openxlsx to write regression outputs to an .xlsx file. The session ends by pointing to a next step: reporting regression results clearly from R output.