4.5 Predictions from the model
For a model with a continuous predictor, each point on the regression line is the estimated mean outcome at a given value of the predictor \((E(Y|X))\), also called the fitted value. For a categorical predictor, the fitted values are the mean outcome values at each level of the predictor. Fitted values are predictions – the predicted value of the outcome at a given value of the predictor. To compute a prediction you could manually enter the predictor value into the model and compute the result, as in the following examples.
Example 4.1 (continued):
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.3041 0.2950 11.200 0
## BMXWAIST 0.0278 0.0029 9.588 0
The predicted mean fasting glucose for those with a waist circumference of 100 cm is approximately 3.3041 + 0.0278 \(\times\) 100 = 6.0841 mmol/L.
Example 4.2 (continued):
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.9423 0.0666 89.229 0.0000
## smokerPast 0.4199 0.1190 3.529 0.0004
## smokerCurrent 0.2551 0.1442 1.769 0.0772
The predicted mean fasting glucose for Current smokers is 5.9423 + 0.4199 \(\times\) 0 + 0.2551 \(\times\) 1 = 6.1974 mmol/L.
However, neither of the above are exact because we rounded each coefficient. Better to let R do the computation for you by using the predict()
function. Repeat the examples above, this time using predict()
, along with interval = "confidence"
which will compute a 95% CI for each prediction. In each case, use the newdata
argument to supply a data.frame
with the value at which we want a prediction.
## fit lwr upr
## 1 6.08 5.984 6.177
Example 4.2 (continued):
## fit lwr upr
## 1 6.197 5.946 6.448
The manual calculation may turn out to be spot on; but this will not always be true due to rounding. If you want an exact answer, and a CI, use predict()
.