1. Please tell true 01' false of the following statements with regard to simple linear regres- sion.(20 points, 2 points each) (a) (b) (C) (d) {6) The least squares line always passes the center of the data (X, Y). If Y : 0, Y : 0, then 50 : 0 no matter What is 5'1. Given the sample size, the larger the range of Xis, the smaller the standard errors of {30,61 tend to be. Under the same condence level, the prediction interval of a new observation is always Wider than the condence interval for the corresponding mean response. A 95% condence interval for 60 based on the observed data is calculated to be [0.3, 0.5]. Therefore P(0.3 g 50 g 0.5) = 0.95. In t-tests, how critical values and pvalues should be derived will depend on the form of the alternative hypothesis. When estimating the mean response corresponding to X13, the further X h is from the sample mean T, the wider the condence interval for the mean response tends to be. If all observations Y} fall on one straight line, then the coeicient of determination R2 = 1. A large R2 always means that the tted regression line is a good t of the data, while a small R2 always means that the predictor and the reSponse are not related. The regression sum of squares SSH tends to be large if the estimated regression slope is large in magnitude or the dispersion of the predictor values is large