Question

In its latest press release, Pill International announced that they are working on a new drug that would stunt the deterioration of brain cells in Alzheimer's patients. If successful, the drug could prolong the life of patients and allow them to retain their basic mobility.

The R&D team is currently testing the drug, which comes in the form of a digestible tablet, for its ability to be dissolved and absorbed in the bloodstream. Based on their latest experiments, they have learned that there is a relationship between the amount of time that the tablet's powder spends in the tray dryer and the amount of time it takes to get dissolved (Y). As a member of this research team, you have been asked to establish the relationship between the two variables and to predict potential dissolution times based on the time spent in the dryer.

Time spent in dryer (seconds) 36 46 68 35 30 23 51 50 33 34 49 67 63 33 47 69 25 62 21 54 60 24 53 70 63 21 64 52 63 27 49 59 54 59 26 58 42 26 24 22 47 68 35 65 64 43 38 49 35 30

Q Dissolution time (seconds) 262.27 262.08 335.27 255.15 -16.89 124.25 251.51 323.76 236.98 276.32 373.7 295.13 216.24 59.28 157.25 258.58 176.12 280.2 93.03 389.59 284.12 116.74 294.84 251.09 163.67 192.16 243.92 324.76 290.24 153.62 166.83 323.7 223.66 395.57 58.84 297.46 196.73 158.1 76.84 121.88 266.38 243.53 155.85 311.31 247.06 113.71 254.24 275.35 135.54 126.47 Regress the time spent in the dryer against the dissolution time. NOTE: Do not change the data values if you have outliers (negative observations) in the data set. Q1- What is your intercept estimate for this model? Enter your answer rounded to two decimal places. For example, if your answer is 12.3456, you should enter 12.35 in the box below. Q2- What is your parameter estimate for this model? Enter your answer rounded to two decimal places. For example, if your answer is 12.3456, you should enter 12.35 in the box below. Q3- If you want to set dryer time to 40 seconds, what would you expect the dissolution time to be (in seconds)? Enter your answer rounded to one decimal place. For example, if your answer is 12.3456, you should enter 12.3 in the box below.

Answer 1

The regression equation is defined as,

The least square estimate of intercept and slope are,

Form the data values, the values are calculated as,

Time spent in dryer (seconds), X	Dissolution time (seconds), Y	X^2	XY
36	262.27	1296	9441.72
46	262.08	2116	12055.68
68	335.27	4624	22798.36
35	255.15	1225	8930.25
30	-16.89	900	-506.7
23	124.25	529	2857.75
51	251.51	2601	12827.01
50	323.76	2500	16188
33	236.98	1089	7820.34
34	276.32	1156	9394.88
49	373.7	2401	18311.3
67	295.13	4489	19773.71
63	216.24	3969	13623.12
33	59.28	1089	1956.24
47	157.25	2209	7390.75
69	258.58	4761	17842.02
25	176.12	625	4403
62	280.2	3844	17372.4
21	93.03	441	1953.63
54	389.59	2916	21037.86
60	284.12	3600	17047.2
24	116.74	576	2801.76
53	294.84	2809	15626.52
70	251.09	4900	17576.3
63	163.67	3969	10311.21
21	192.16	441	4035.36
64	243.92	4096	15610.88
52	324.76	2704	16887.52
63	290.24	3969	18285.12
27	153.62	729	4147.74
49	166.83	2401	8174.67
59	323.7	3481	19098.3
54	223.66	2916	12077.64
59	395.57	3481	23338.63
26	58.84	676	1529.84
58	297.46	3364	17252.68
42	196.73	1764	8262.66
26	158.1	676	4110.6
24	76.84	576	1844.16
22	121.88	484	2681.36
47	266.38	2209	12519.86
68	243.53	4624	16560.04
35	155.85	1225	5454.75
65	311.31	4225	20235.15
64	247.06	4096	15811.84
43	113.71	1849	4889.53
38	254.24	1444	9661.12
49	275.35	2401	13492.15
35	135.54	1225	4743.9
30	126.47	900	3794.1
Sum=2286	Sum=11074.03	Sum=116590	Sum=553333.9

Q1)

Q2)

Q3)

For X = 40,