Problem 12. Wells, Rufus M. G. and Pankhurst, Ned W. (1999, Evaluation of simple instruments for the measurement of blood glucose and lactate, and plasma protein as stress indicators in fish, Journal of The World Aquaculture Society 30(2), 276-284) described an experiment in which fish were subjected to stress protocol and then removed and tested at various times after the protocol had been applied. Here are the data on time (in minutes) and blood glucose level (mmol/L) from 24 randomly selected fish. Assume that a simple linear regression model is appropriate for modeling the relationship between glucose and time of stress protocol. Time: 2, 2, 5, 7, 12, 13, 17, 18, 23, 24, 26, 28, 29, 30, 34, 36, 40, 41, 44, 56, 56, 57, 60, 60 Glucose: 4.0, 3.6, 3.7, 4.0, 3.8, 4.0, 5.1, 3.9, 4.4, 4.3, 4.3, 4.4, 5.8, 4.3, 5.5, 5.6, 5.1, 5.7, 6.1, 5.1, 5.9, 6.8, 4.9, 5.7. R output of linear regression of glucose on time Coefficients: Estimate Std. Error t value Pr(>|t|) Intercept 3.696487 0.215919 17.120 3.34e-14 Time 0.037895 0.006137 6.174 3.25e-06 Residual standard error: 0.5525 on 22 degrees of freedom Multiple R-squared: 0.6341, Adjusted R-squared: 0.6174 F-statistic: 38.12 on 1 and 22 DF, p-value: 3.251e-06 a. Write out the estimated linear regression equation. b. What portion of variation in blood glucose can be explained by the linear relationship between time and glucose? c. Is there a significant linear relationship between time and blood glucose level at 0.05 level of significance? Write out your hypotheses and P-value. d. Construct an interval for which you are 95% confident that the change of mean blood glucose level with 1-minute increase of time for stress protocol lies between the limits of the interval. e. Construct an interval for which you are 95% confident that the mean blood glucose level after a 5-minute stress protocol lies between the limits of the interval. f. Construct an interval for which you are 95% confident that an individual blood glucose level after a 5-minute stress protocol lies between the limits of the interval.