Hello could you help the problem below step by step in R please? Data is at the very bottom.

Consider the longitudinal study data (diabetes.dat) from an experiment conducted by a diabetes researcher who was interested in comparing the blood sugar reduction in rabbits after being treated by three different insulin mixtures. The study involved a total of 36 rabbits, where 12 rabbits were randomly assigned to each of the 3 treatment groups: group 1: standard insulin mixture; group 2: a mixture containing 1% less protamine than the standard; group 3: a mixture containing 5% less protamine. 1 Rabbits were injected with the assigned mixture at time 0, and blood sugar measurements were taken on each rabbit at the time of injection (time 0) and 0.5, 1.0, 1.5, 2.5, and 3.0 hours post-injection.

The dataset has 4 columns: (1) rabbit number (RabbitNum), (2) time (Hours), (3) response blood sugar level (BloodSugar), and (4) insulin mixture group (InsulinGrp). We are interested in whether the rate of change of blood sugar level over time is similar for 3 insulin groups.

• (a) Plot the time course trajectory for each rabbit and separate by insulin group (generate 3 spaghetti plots, one for each insulin treatment group).
• (b) Plot the mean time course trajectory for each treatment group and put all three mean trajectories into one graph. Does the plot suggest a linear relationship between the blood sugar level and time for each treatment group?
• (c) Suppose we assume every observation (blood sugar) is independent (even within the same rabbit). Fit a linear regression model with blood sugar being the outcome variable, and time (hours) being the continuous predictor, allowing both intercepts and slopes to be different for the three treatment groups. Based upon the above model, perform the hypothesis testing on (i) whether the intercepts are the same for all 3 treatment groups; (ii) whether the slopes are the same for all 3 treatment groups.
• (d) Now we account for the correlations among the measures at different time points within the same rabbit and consider a random slope model. Based upon this mixed-effect model, perform the hypothesis testing on (i) whether the intercepts are the same for all 3 treatment groups; (ii) whether the slopes are the same for all 3 treatment groups.

RabbitNum Hours BloodSugar InsulinGrp 1 0.0 78.1 1 1 0.5 68.3 1 1 1.0 77.5 1 1 1.5 76.4 1 1 2.0 70.7 1 1 2.5 69.8 1 1 3.0 57.8 1 2 0.0 124.2 1 2 0.5 97.1 1 2 1.0 85.2 1 2 1.5 66.6 1 2 2.0 66.3 1 2 2.5 62.2 1 2 3.0 59.9 1 3 0.0 106.2 1 3 0.5 108.7 1 3 1.0 94.7 1 3 1.5 78.4 1 3 2.0 88.1 1 3 2.5 85.9 1 3 3.0 66.9 1 4 0.0 92.5 1 4 0.5 82.9 1 4 1.0 90.0 1 4 1.5 87.8 1 4 2.0 75.3 1 4 2.5 73.7 1 4 3.0 69.4 1 5 0.0 116.2 1 5 0.5 110.2 1 5 1.0 95.1 1 5 1.5 81.3 1 5 2.0 58.8 1 5 2.5 52.5 1 5 3.0 49.1 1 6 0.0 104.8 1 6 0.5 85.0 1 6 1.0 81.1 1 6 1.5 80.0 1 6 2.0 73.6 1 6 2.5 62.6 1 6 3.0 59.9 1 7 0.0 107.5 1 7 0.5 111.0 1 7 1.0 80.7 1 7 1.5 87.9 1 7 2.0 71.4 1 7 2.5 56.6 1 7 3.0 61.5 1 8 0.0 118.5 1 8 0.5 97.0 1 8 1.0 78.0 1 8 1.5 64.0 1 8 2.0 62.3 1 8 2.5 73.9 1 8 3.0 76.6 1 9 0.0 79.8 1 9 0.5 82.6 1 9 1.0 75.5 1 9 1.5 65.8 1 9 2.0 67.9 1 9 2.5 60.0 1 9 3.0 65.1 1 10 0.0 95.7 1 10 0.5 91.7 1 10 1.0 69.1 1 10 1.5 69.2 1 10 2.0 72.3 1 10 2.5 83.7 1 10 3.0 80.9 1 11 0.0 88.0 1 11 0.5 80.9 1 11 1.0 70.5 1 11 1.5 75.7 1 11 2.0 63.8 1 11 2.5 58.3 1 11 3.0 57.1 1 12 0.0 97.9 1 12 0.5 83.5 1 12 1.0 100.1 1 12 1.5 76.1 1 12 2.0 52.0 1 12 2.5 50.6 1 12 3.0 69.1 1 13 0.0 103.0 2 13 0.5 78.1 2 13 1.0 69.8 2 13 1.5 61.4 2 13 2.0 70.9 2 13 2.5 56.9 2 13 3.0 63.5 2 14 0.0 82.2 2 14 0.5 74.9 2 14 1.0 80.3 2 14 1.5 61.5 2 14 2.0 57.3 2 14 2.5 47.9 2 14 3.0 65.3 2 15 0.0 116.2 2 15 0.5 78.1 2 15 1.0 84.8 2 15 1.5 67.0 2 15 2.0 61.0 2 15 2.5 45.7 2 15 3.0 45.0 2 16 0.0 107.4 2 16 0.5 88.0 2 16 1.0 69.7 2 16 1.5 65.8 2 16 2.0 47.5 2 16 2.5 43.3 2 16 3.0 28.6 2 17 0.0 83.5 2 17 0.5 95.2 2 17 1.0 83.7 2 17 1.5 77.0 2 17 2.0 58.2 2 17 2.5 59.4 2 17 3.0 43.7 2 18 0.0 104.1 2 18 0.5 75.0 2 18 1.0 62.0 2 18 1.5 66.6 2 18 2.0 62 2 18 2.5 51.4 2 18 3.0 35.0 2 19 0.0 114.9 2 19 0.5 99.3 2 19 1.0 83.1 2 19 1.5 68.8 2 19 2.0 63.7 2 19 2.5 52.2 2 19 3.0 36.8 2 20 0.0 117.0 2 20 0.5 81.2 2 20 1.0 84.1 2 20 1.5 58.7 2 20 2.0 53.6 2 20 2.5 72.1 2 20 3.0 53.8 2 21 0.0 95.7 2 21 0.5 68.5 2 21 1.0 59.7 2 21 1.5 71.8 2 21 2.0 53.5 2 21 2.5 52.2 2 21 3.0 60.5 2 22 0.0 100.3 2 22 0.5 85.2 2 22 1.0 74.1 2 22 1.5 70.4 2 22 2.0 65.1 2 22 2.5 44.3 2 22 3.0 54.0 2 23 0.0 98.4 2 23 0.5 89.5 2 23 1.0 70.7 2 23 1.5 71.8 2 23 2.0 51.7 2 23 2.5 41.2 2 23 3.0 42.5 2 24 0.0 103.1 2 24 0.5 94.1 2 24 1.0 90.3 2 24 1.5 62.3 2 24 2.0 53.6 2 24 2.5 51.2 2 24 3.0 57.9 2 25 0.0 112.7 3 25 0.5 102.4 3 25 1.0 110.1 3 25 1.5 63.5 3 25 2.0 60.5 3 25 2.5 63.2 3 25 3.0 49.0 3 26 0.0 106.8 3 26 0.5 88.1 3 26 1.0 75.6 3 26 1.5 72.6 3 26 2.0 48.9 3 26 2.5 46.9 3 26 3.0 60.2 3 27 0.0 115.1 3 27 0.5 95.0 3 27 1.0 88.2 3 27 1.5 77.9 3 27 2.0 74.4 3 27 2.5 58.8 3 27 3.0 56.9 3 28 0.0 106.0 3 28 0.5 96.8 3 28 1.0 72.3 3 28 1.5 76.5 3 28 2.0 77.1 3 28 2.5 60.5 3 28 3.0 56.6 3 29 0.0 101.1 3 29 0.5 96.4 3 29 1.0 85.1 3 29 1.5 78.6 3 29 2.0 59.3 3 29 2.5 62.9 3 29 3.0 42.2 3 30 0.0 108.9 3 30 0.5 88.7 3 30 1.0 76.3 3 30 1.5 66.9 3 30 2.0 44.6 3 30 2.5 71.4 3 30 3.0 50.2 3 31 0.0 114.4 3 31 0.5 90.0 3 31 1.0 85.2 3 31 1.5 82.8 3 31 2.0 73.2 3 31 2.5 62.5 3 31 3.0 43.3 3 32 0.0 103.5 3 32 0.5 86.9 3 32 1.0 70.8 3 32 1.5 79.0 3 32 2.0 74.7 3 32 2.5 50.2 3 32 3.0 40.1 3 33 0.0 99.7 3 33 0.5 82.3 3 33 1.0 71.6 3 33 1.5 83.5 3 33 2.0 71.9 3 33 2.5 52.5 3 33 3.0 49.7 3 34 0.0 95.0 3 34 0.5 92.8 3 34 1.0 70.7 3 34 1.5 74.6 3 34 2.0 57.9 3 34 2.5 59.2 3 34 3.0 35.9 3 35 0.0 113.3 3 35 0.5 95.4 3 35 1.0 85.6 3 35 1.5 51.4 3 35 2.0 57.8 3 35 2.5 50.1 3 35 3.0 61.0 3 36 0.0 85.6 3 36 0.5 96.9 3 36 1.0 99.5 3 36 1.5 77.9 3 36 2.0 46.9 3 36 2.5 45.5 3 36 3.0 51.5 3