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.![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,  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,](/WebImages/3/consider-a-linear-regression-of-response-variable-y-y1-ynon-973128-1761499843-0.webp) 
  
  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,  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,](/WebImages/3/consider-a-linear-regression-of-response-variable-y-y1-ynon-973128-1761499843-0.webp)
