Linear Regression Calculator

Your details

The independent (predictor) values, separated by commas.
The dependent (response) values, in the same order as the x values.
Used to compute confidence and prediction intervals and to flag statistical significance.
Enter an x value to get the predicted y, confidence interval for the mean, and prediction interval for a single new observation.
When enabled the line is constrained to pass through the origin: y = mx. Use only when theory demands it.
Slope (m)Strong fit
0.8
Intercept (b)1.8
r² (coefficient of determination)0.7273
Correlation (r)0.8528
Std error of estimate (Se)0.8944
t-statistic (slope)2.8284
p-value (slope)0.009
F-statistic (overall)8
p-value (F-test)0.009
Data points (n)5
Predicted y4.2
Confidence interval (low)-15.8
Confidence interval (high)24.2
Prediction interval (low)-44.7898
Prediction interval (high)53.1898
0.7273 r^2
Poor fit<0.3Weak fit0.3-0.5Moderate fit0.5-0.7Strong fit0.7-0.9Very strong fit0.9+

Best-fit line: y = 0.8x + 1.8 (r^2 = 0.7273, n = 5).

  • The slope of 0.8 means y rises by about 0.8 for every one-unit increase in x.
  • r^2 = 0.7273 - the line explains roughly 72.7% of the variation in y; the rest is unexplained scatter.
  • The standard error of the estimate is 0.8944, the typical distance between an observed y and the fitted line.
  • The overall F-test is statistically significant (p < 0.05), meaning the slope is unlikely to be zero by chance.
  • With only 5 points the estimates are imprecise; more data will narrow the intervals.

Next stepAt your chosen x, y-hat = 4.2. The 95% confidence interval for the mean response is [-15.8, 24.2] and the prediction interval for a new single observation is [-44.7898, 53.1898].

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