Consider a linear regression of response variable Y Y1 Ynon

Consider a linear regression of response variable Y = [Y1,....., Yn]on a predictor variable X = [X1,...Xn]. The least-squares estimates of intercept and slope, alpha and Beta are the values minimizing the function: d(alpha, Beta) = Sigma n to i = 1{Yi - (alpha + Beta xi,)}^2 Further, predicted values are y(x) = alpha + Beta x. Find y(X), where X is the average of the Xi is.

Solution

 Consider a linear regression of response variable Y = [Y1,....., Yn]on a predictor variable X = [X1,...Xn]. The least-squares estimates of intercept and slope,

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