# The interval estimate of the mean value of y for a given value of x is the?

**Solution:**

The Interval estimate of the mean value of y for a given value of x is termed as the confidence interval estimate.

This concept arises from the subject of regression analysis. Let us for example consider y as function of x and denoted by the equation below:

y = f(x) --- (1)

In the above equation y is the explained variable and x is the explanatory variable. Let us assume for a while that the relationship between y and x is a linear relation and expressed by the equation below as:

yi = α + βxi + ui, i = 1, 2, 3, 4…...n --- (2)

The above relation is a statistical relationship which does not give unique values of y for given values of x but can be described in probabilistic terms. u is the error term which causes the variation in the explained variable y.

In other words the above equation is a stochastic equation in which u is the error term and it has a probability distribution. The error term is normally distributed and Σui = 0.

The terms xi and yi are observed from the environment and on the basis of the values of obtained for xi and yi the regression coefficients ɑ and β can be estimated and regression equation of the form y = α + βx + u can be arrived at.

Since it is a stochastic equation the value of y will be expressed in the form of interval estimate which will be based on the confidence levels chosen for interval estimate e.g. 95% , 99.5% confidence limits.

## The interval estimate of the mean value of y for a given value of x is the?

**Summary:**

The Interval estimate of the mean value of y for a given value of x is termed as the confidence interval estimate.

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