Question

If the prediction interval obtained so wide. How could we reduce the width of the interval?

Answer 1

Prediction intervals tell you where you can expect to see the next data point sampled. Assume that the data really are randomly sampled from a Gaussian distribution. Collect a sample of data and calculate a prediction interval. Then sample one more value from the population. If you do this many times, you'd expect that next value to lie within that prediction interval in 95% of the samples.The key point is that the prediction interval tells you about the distribution of values, not the uncertainty in determining the population mean.

Prediction intervals must account for both the uncertainty in knowing the value of the population mean, plus data scatter. So a prediction interval is always wider than a confidence interval.

We can reduce the width of prediction interval by increasing the sample size which gives us better population estimates and reduces the standard error due to which we can predict confidently within a smaller interval