For the following data X 30 28 41 18 30 45 Y 130.4 125.0 163.3 94.4 130.4 173.9 (a) Estimate the regression equation of Y on X using OLS. (b) Estimate and interpret the increase in Y for a unit increase in X. (c) What value of Y would you predict for X=40? Why this value? (d) Calculate the residual for the fourth observation, e4, where X=18. (e) Does the estimated regression line pass through mean values of x and y ? (f) Find the sample mean of y and y. Are they always the same? (g) Compute the correlation between the X variable and the estimated residual. Explain the result. (h) Compute the expected (mean) value of the estimated residuals. Is the mean equal to zero?