Lesson 7 of 9 · All lessons in this module
  1. The regression model and least squares
  2. Interpreting coefficients, fitted values and residuals
  3. The four assumptions and residual plotsVideo lesson
  4. Sums of squares, \(R^2\), the ANOVA table and the SEEVideo lesson
  5. Testing the slope: t-test, correlation test and F-testVideo lesson
  6. Intercept tests, indicator variables and p-values
  7. Forecasts and prediction intervals
  8. Functional forms: log-lin, lin-log and log-logVideo lesson
  9. Integrated cases: reading a full regression printout

Lesson 7 of 9 · 13 min

Forecasts and prediction intervals

A forecast is a point on the fitted line; the prediction interval around it widens with the SEE, with a small sample and with how far the forecast X is from the mean of X.

In short

  • Point forecast: Y^f=b^0+b^1Xf\hat Y_f = \hat b_0 + \hat b_1X_f.
  • The standard error of the forecast sfs_f is always larger than ses_e: it adds uncertainty about the estimated line itself.
  • sfs_f is smaller with a better fit (lower ses_e), a larger n, more variation in X, and an XfX_f closer to Xˉ\bar X.
  • Prediction interval: Y^f±tc×sf\hat Y_f \pm t_c \times s_f, with n − 2 df and tct_c for α/2\alpha/2 in each tail.
  • A higher confidence level gives a larger tct_c and a wider interval.

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