Model relationships quickly with clean linear regression outputs. Paste paired data and verify predictions fast. Export results, review fit, and improve decisions today confidently.
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Simple regression summarizes how one input explains one outcome. It returns a slope and intercept that minimize squared residuals, giving a transparent baseline before adding more variables. With n observations, the model produces fitted values ŷ that can be compared to actual y to see pattern strength and noise.
The slope b represents expected change in y for a one unit increase in x. If b = 1.8, moving x from 10 to 11 increases ŷ by 1.8 in the same units as y. The intercept a is the predicted value when x equals zero; it is meaningful only when zero lies in the data’s realistic range. Use consistent units and check that x values cover the operating domain you care about.
R² describes the fraction of variation explained by the fitted line. An R² of 0.72 means 72% of the variability around ȳ is captured by the model, leaving 28% unexplained. SSE totals squared residuals, while RMSE converts average squared error back into y units for intuitive comparison across datasets. MSE equals SSE divided by degrees of freedom, n−2 with an intercept, and it supports standard errors.
Some processes are physically constrained to pass through (0,0), such as proportional scaling or calibration without offset. In that case, setting a = 0 can reduce variance and simplify interpretation. However, a no-intercept fit changes R² to an uncentered form, so compare models using SSE or RMSE when that option is used. If your data include measurement bias, forcing the origin can worsen predictions even when it looks neat.
Prediction uses ŷ = a + b·x, but uncertainty increases as x moves away from the observed range. Treat extrapolation cautiously and review residuals for systematic bias. The slope t-statistic helps gauge whether b is distinguishable from zero when assumptions are reasonable and n is adequate. For reporting, export CSV to audit inputs and fitted values, or create a PDF snapshot for stakeholders and documentation.
The slope is the estimated change in y for each one unit increase in x. A positive slope indicates y rises as x rises, while a negative slope indicates an inverse relationship.
R² estimates the proportion of variation in y explained by the line. Higher values indicate better fit, but a high R² does not guarantee correct causality or good out-of-range predictions.
Include an intercept for most real datasets because offsets and baseline effects are common. Only force the origin when theory or measurement design clearly requires the relationship to pass through (0,0).
If x does not vary, the slope cannot be estimated because the line is undefined. Add more diverse x values or verify your data import to ensure multiple distinct x points exist.
CSV downloads a table of metrics plus fitted values and residuals. PDF captures the on-screen results panel as a snapshot, which is useful for sharing or attaching to reports.
At least two points are required to fit a line, but more points improve stability. For standard errors and the slope t-statistic, you need at least three points and preferably many more.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.