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21) Can your life expectancy be predicted from the gestational age that you were born at? A large longitutional study looked at the age

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21) Can your life expectancy be predicted from the gestational age that you were born at? A large longitutional study looked at the age adults were when they died from natural causes (in years) and the gestational age they were when they were born (in weeks). Gestational age is the common term used during pregnancy to describe how far along the pregnancy is. Below, there is a table of the data, a scatterplot of the data, a residual plot, and a dotplot of the data. Gestational Age Age at Death 84- 26.6 78.7 83.5- 35.4 78.8 83- 35.3 79 35.5 79.1 28.8 79.3 27.7 79.5 28.3 79.8 37.0 80.1 31.4 80.2 Age at Death (Years) 82.5- 82- 81.5- 81- 80.5- 80- 34.0 80.7 33.7 81 79.5- 32.2 81 79- 32.3 81.2 78.5- 34.3 81.7 26 28 30 32 34 36 38 40 37.0 81.7 Gestational Birth Age (Weeks) 31.8 81.5 32.5 82.1 40.8 82.2 35.3 82.8 38.8 83.1 33.6 83.3 Residual 33.6 83.2 38.3 83.5 36.3 83.8 26 28 30 32 34 36 38 40 Gestational Birth Age (Weeks) 38.3 83.6 36.1 83.8 33.4 84 35.4 83.7 800808 8000 36.9 84.1 -3 -2.5 T -2 -1.5 -1 40.1 84 -0.5 Residual 0 0.5 1 1.5 2 2.5 (a) What is the equation of the least-squares regression line based on these data? Define any variables used. (b) Interpret the slope of the regression line. (c) Are the conditions needed to perform inference using t-procedures met? Explain. (d) Assuming all conditions have been met, construct and interpret a 90% confidence interval for the slope of the least squares regression of age at death on gestational birth age. 1.5 B0 (e) If you were to perform a test of the hypotheses Ho: =0 and Ho: 0 at a =0.10 level, what would you conclude? Justify your answer using your result in part (d).

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