a. interpret the corresponding 95% confidence intervals for both Birth weight and Age. b. What is the predicted average SBP of an infant born with birth weight 8lbs (128oz) measured at 3 days old? c. Calculate the Pearson correlation between Age and Birth weight, and test if this correlation is significant at the 0.05 level. Does this answer surprise you, why or why not? SHOW ALL WORK. Interpret confidence intervals and explain the conclusionsfrom hypothesis tests. For all hypothesis tests, clearly state the null andalternative hypotheses, the significance level, the test statistic, the p-value, andyour conclusion. If you are using a t-statistic, clearly note how many degrees offreedom you have.1. Consider the following data collected regarding infant blood pressure, age, andbirth weight:12345678910111213141516Birth weight inoz. (x1)1351201001051301251251051209012095120150160125Age indays (x2)343245235423343 3Systolic Blood PressuremmHg (y)89908377929882859695807986979288

Given data: x1 x2 y 135 3 89 120 4 90 100 3 83 105 2 77 130 4 92 125 5 98 125 2 82 105 3 85 120 5 96 90 4 95 120 2 80 95 3 79 120 3 86 150 4 97 160 3 92 125 3 88a) The objective is to interpret the corresponding 95% confidence intervals for both Birth weight and Age. The 95% confidence intervals for regression coefficients of the model can be obtained using R. R code: Output: Based on the above output, the 95% confidence interval for Birth weight is: (0.0514, 0.1998). The 95% confidence interval for Age is: (4.4182, 7.3572). Interpretation: One can be 95% confident that the actual slope β1 corresponding to birth weight i.e., the average unit change in SBP based on one unit change in birth weight holding age constant lies between (0.0514, 0.1998). One can be 95% confident that the actual slope β2 corresponding to Age i.e., the average unit change in SBP based on one unit change in Age holding birth weight constant lies between (4.4182, 7.3572). (b) The objective is to find the predicted average SBP of an infant born with birth weight 128oz measured at 3 days old: R code: Output: Thus, the predicted average SBP of an infant born with birth weight 128oz measured at 3 days old is approximately 87 mmHg. (c) The relevant hypotheses are: Null Hypothesis H0:ρ=0 i.e., there is no association between Age and Birth weight. Alternative Hypothesis H1:ρ≠0 i.e., there is an association between Age and Birth weight. R code: Output: The Pearson correlation coefficient between Age and Birth weight is 0.10683 Since the p-value (0.6937) is greater than the significance level (0.05), we fail to reject H0. Thus, the correlation is not significant. In reality, there cannot be any association between Birth weight and age of an infant. Birth weight is fixed for a person and does not change as age increases. Hence, the answer obtained is not surprising.