Consider a regression problem for the response y with 2 predictors x, and x2. The model is given by y = Bot BIX1 + B2X2 + E where (Bo. Bi. B2) are the model parameters and e is the error term which is an unobservable random variable (independent of the predictors) with mean zero and constant variance. The variables used are listed below. Variable* Description Weight The baby's birth weight in ounces Gestation The duration of pregnancy in days. Smoking The indicator for mother's smoking status (1=smoker, 0=non-smoker). This is a reduced version of the original dataset taken from Stat Labs by Nolan and Speed from the Child Health and Development Studies conducted at the Oakland, CA, Kaiser Foundation Hospital. Then the training dataset { (X,1, X/2, )(): / = 1,...200 ) has been used to get the following least-squares estimates: Coefficients: Estimate Std. Error t value (Intercept) 2.8029 18. 8752 0.1485 Gestation 0. 4383 0. 0675 6. 4901 Smoking -8.5512 2. 1561 2 Residual standard error: 14.51 on 197 degrees of freedom [ 3 PTS ] Write down the regression equation of the red line in Figure 2.1 using the resulting R print-out above. State the effect of mother's smoking status on the baby's birth weight. 160 140 Weight (in ounces) 100 80 220 240 260 280 300 320 340 Gestation (in days) Figure 2.1 The scatterplot of the data with the fitted regression line.[3 PTS ] Find the average birth weight in ounces for a baby who was delivered after 50 weeks as a gestational period for a smoker mother. [ 4 PTS ] Calculate the 99% confidence interval for the parameter , and use it to test the hypothesis Ho: 1 = 0 at 1% level of significance (use the 2.35 as the critical value). State in words the implication of your conclusion on the importance of the relevant predictor on determining the baby's birth weight. [4 PTS ] Write down the value of the RSS and the missing t-value