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A researcher collected data on length at birth (x) and the length at six months (y) for eight infants. infant 1 2 3 4 5 6 7 8 birth length (inches) 19.75 20.5 19 21 19 18.5 20.25 20 6month length (inches) 25.5 26.25 25 26.75 25.75 25.25 27 26.5 We previously found the least squares equation, 1): 12.03 +0.7073 x , and the AN OVA table: Source df SS MS F Regression 1 2.5640 2.5640 12.97 Error 6 1.1860 0.1977 Total 7 3.7500 Note: you may do the following calculations either by hand or on the computer. a) (4) Determine the 95% confidence interval for the mean length at siXamonths for all babies born at 20 inches. Recall SSxx = 5.125. b) (4) Suppose that a new infant is born at 20 inches long. Predict the length this infant will be at six months. Determine a 95% prediction interval for an infant born at 20 inches long. c) ( 1) Why is the prediction interval from part (b) wider than the confidence interval in part (a)? d) (5) Suppose that a new infant is born at 18 inches long. Determine the 95% prediction interval for this infant. Why is this interval wider than the one in part (b)? e) (2) Determine the coefficient of determination, R2. How well does this model explain the variation in lengths at six months? 0 (4) On the back is the 4in1 plot from Minitab. Are there any indications of problems with the assumptions of normality, linearity, variation, or independence? Why or why not