Question

Solve the problem.

A regression equation can be used to make predictions of the y value corresponding to a particular x value. Determine whether the following statement is true or false:

The 95% confidence interval for the mean of all values of y for which x = x0 will be wider than the 95% confidence interval for a single y for which x = x0.

Answer 1

Confidence intervals tells you about how you have determined the mean. Assume that the data really are randomly sampled from a Gaussian distribution. If you do this a lot many times, and calculate a confidence interval of the mean from each sample, you'd expect about 95 % of those intervals to include the true value of the population mean.

The key point is that the confidence interval tells you about the likely location of the true population parameter.

Prediction intervals tells us where we 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.

hope you would understand the definations.!!