Question

Traditional methods that forensic investigators use to determine human age require the destructive testing of bones or teeth. This presents a problem for crime scene investigators when the body of the deceased is not available.

A recently developed DNA-based blood test now enables forensic investigators with only a drop of blood for evidence to determine the age of the person who was bleeding. The test also works on dried bloodstains even those revealed by a heat-vision camera. This could help detectives reopen cases that went cold years ago.

This Excel file Blood Test for Age has data on the DNA-based blood test measurements of 321 volunteer human subjects with known ages from just under 2 to just over 96.

We would like to use a linear model to model the relationship between the blood test measurements and human age. A scatterplot of the data with the blood test measurements as the explanatory (x) variable and age as the response (y) variable indicates that a linear model is appropriate. I suggest you create your own scatterplot to verify this and to better understand the data.

Question 3. Help Holmes solve this murder mystery by calculating a 90% prediction interval for the age of the person whose blood is on the golf club (use 2 decimal places).

lower bound of prediction interval
upper bound of prediction interval

Question 4. The murdered wealthy philanthropist was 35 years old. The police chief would like to know if the golf club found by Holmes could possibly be the murder weapon. What should Holmes tell the police chief? (One submission only).

A 90% confidence interval will indicate that it is more likely that the blood on the golf club is from the murdered philanthropist.The golf club is probably not the murder weapon since it is unlikely that the blood on the golf club is from a person whose age is similar to that of the murdered philanthropist.    The golf club could be the murder weapon since there is statistically valid evidence that the blood on the golf club is from a person similar in age to the murdered philanthropist.

Blood Test Measure	Age in Years
-15.49	78.2
-11.04	51.3
-13.62	70.1
-7.79	7.6
-14.84	77.9
-8.3	20.1
-9.83	24.4
-15.12	65.7
-13.31	55
-14.66	72.5
-15.77	63
-15	64.7
-10.45	38.7
-7.68	26.1
-15.93	76.2
-6.06	17.3
-16.82	77.6
-16.74	68.1
-14.83	80.5
-8.82	27.7
-9.72	32.2
-15.54	79.9
-7.5	14.3
-6.55	15.4
-12.21	56.8
-10.57	51.4
-11.12	42.3
-5.92	5
-8.03	18.5
-7.72	23
-5.04	2.9
-5.98	4.8
-8.06	10.1
-9.55	39.9
-6.14	11.1
-15.3	81.4
-9.55	20.3
-13.03	52.1
-6.42	7.7
-11.92	59.8
-6.8	22.3
-13.38	53.4
-12.92	64.8
-15.49	72.2
-12.97	66.1
-12.53	39
-12.22	65
-9.6	29
-11.42	24.6
-16.3	88.6
-10.16	46.2
-15.13	66.9
-10.42	23.8
-8.94	22.3
-6.76	16.7
-5.13	1.7
-13.74	64.1
-15.41	62.7
-9.8	27.3
-8	32.8
-9.43	25.4
-13.14	52.9
-15.58	62.9
-6.85	3.3
-8.11	27.2
-15.89	78.7
-14.95	59
-11.92	58
-7.56	31.7
-14.65	77.1
-16.08	80.9
-10.8	55.5
-15.83	48.8
-14.85	65.3
-9.17	47.6
-11.84	65.1
-10.26	40.3
-5.36	7.2
-8.25	11.4
-8.66	45.6
-16.63	82.8
-9.72	32.6
-11.91	59.5
-11.13	39.9
-10.3	37.9
-8.5	14.8
-4.91	4.1
-13.16	61.6
-9.33	21.5
-8.97	41.5
-16.03	68.9
-9.98	13
-11.02	37.6
-9.15	21.6
-11.36	35.4
-5.3	4.9
-11.85	43.6
-11.3	44.3
-11.14	35.8
-8.55	31.2
-12.48	50.8
-9.41	39.8
-9.88	44.7
-5.54	7.8
-7.08	16.7
-14.03	69.4
-10.49	39.3
-16.05	79.6
-6.97	8.3
-8.17	25.2
-5.64	11.3
-10.5	45.6
-7.85	33
-11.88	52.4
-9	27.9
-11.05	50.6
-6.99	10.7
-10.99	25.8
-15.28	78.6
-9.29	46.8
-10.6	39.5
-6.77	4.2
-12.58	46.2
-8.57	21.9
-10.86	19.3
-7.17	10.7
-11.02	42
-5.64	17.2
-8.16	22.1
-7.34	27.1
-9.31	26.5
-15.6	80.8
-10.55	31.9
-14.62	74.2
-12.88	45.3
-13.53	58.8
-13.05	48.2
-12.51	40
-9.19	16.7
-11.46	30.2
-12.37	51.9
-12.94	59.3
-5.2	6.9
-6.15	32.7
-14.37	72.2
-12.83	60.9
-14.31	65.8
-7.27	22.5
-10.6	46.6
-8.58	35.6
-14.21	72
-11.18	44.6
-6	20.9
-7.19	26.1
-14.62	68.5
-10.99	44.5
-8.77	31.2
-16.13	81
-9.64	18.7
-15.49	70.3
-11.04	32.8
-13.62	53.3
-7.79	31.4
-14.84	72.2
-8.3	12
-9.83	51.2
-15.12	83.3
-13.31	67.7
-14.66	63.2
-15.77	69.8
-15	62.5
-10.45	36.2
-7.68	32.6
-15.93	69.6
-6.06	10
-16.82	70.2
-16.74	71.5
-14.83	81.6
-8.82	33.1
-9.72	26.4
-15.54	63.3
-7.5	15.2
-6.55	10
-12.21	48.5
-10.57	29.3
-11.12	36.6
-5.92	5
-8.03	20.4
-5.77	14.5
-7.72	31.9
-8.06	13
-9.55	37.5
-6.14	15.2
-15.3	79.4
-9.55	25.9
-13.03	49.1
-6.42	5.9
-11.92	61.2
-6.02	6.7
-6.8	14.1
-13.38	54.8
-12.92	60.1
-15.49	69.4
-12.97	52.6
-12.53	49.6
-12.22	54.8
-9.6	36.1
-11.42	54.2
-16.3	83.5
-10.16	40.5
-15.13	71.2
-6.44	12.2
-10.42	34
-8.94	25.5
-6.76	7.1
-13.74	38.9
-15.41	70.1
-9.8	35.3
-8	24
-9.43	26.6
-13.14	66.1
-15.58	60.9
-6.85	22.9
-8.11	22.2
-7.26	12
-15.89	62.8
-14.95	61.6
-11.92	53.2
-7.56	29.5
-14.65	65.3
-16.08	79.7
-10.8	45.3
-15.83	79.2
-14.85	65
-9.17	37.2
-11.84	38.3
-10.26	37.2
-8.25	27.4
-8.66	28.7
-16.63	96.2
-9.72	33.1
-11.91	44.5
-11.13	47.6
-10.3	38.4
-8.5	26.9
-4.91	8.4
-13.16	56
-9.33	22.6
-8.97	20
-16.03	78.1
-9.98	21.8
-3.84	10.6
-11.02	35
-9.15	21.3
-11.36	30.6
-5.3	5.7
-11.85	39.6
-11.3	33.3
-11.14	53.4
-8.55	19.1
-12.48	48.9
-9.41	56.4
-9.88	45.8
-5.54	1.9
-7.08	16.3
-14.03	69.7
-10.49	36.1
-16.05	77.9
-6.97	19.2
-8.17	31.4
-5.64	7.2
-5.73	8.5
-10.5	39
-7.85	14
-11.88	48.5
-9	40.8
-11.05	41.6
-6.99	20.5
-10.99	59.3
-15.28	77
-9.29	45.1
-10.6	35.7
-6.77	4.7
-12.58	63.8
-8.57	30.8
-10.86	51.3
-7.17	12.8
-11.02	48.8
-8.16	32.4
-7.34	21.2
-9.31	34.5
-4.58	22.5
-15.6	71.4
-10.55	37
-14.62	61.8
-12.88	66.3
-13.53	66.4
-13.05	54.2
-12.51	39.9
-9.19	30.5
-11.46	38.4
-12.37	58.2
-12.94	61.5
-3.41	2.4
-6.15	7.9
-14.37	82.6
-12.83	56
-14.31	65.5
-7.27	3.5
-10.6	41.8
-8.58	23.9
-14.21	62.2
-11.18	32.8
-5.14	3.5
-6	11.2
-7.19	24.2
-14.62	56.3
-10.99	54.6
-8.77	27.4
-16.13	64.7
-9.64	34.2

Answer 1

THis scatter plot shows a negative relationship in variables.

Linear model output is

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.928555
R Square	0.862215
Adjusted R Square	0.861783
Standard Error	8.441812
Observations	321
ANOVA
	df	SS	MS	F	Significance F
Regression	1	142257.1	142257.1	1996.193	2.4E-139
Residual	319	22733.28	71.26419
Total	320	164990.3
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-28.3431	1.625332	-17.4384	2.67E-48	-31.5409	-25.1454
Blood Test	-6.46363	0.144669	-44.6788	2.4E-139	-6.74825	-6.179

Q 3.

90% prediction interval of the forecasted value

where

Lower bound is

Upper bound is

Q4

The golf club is probably not the murder weapon since it is unlikely that the blood on the golf club is from a person whose age is similar to that of the murdered philanthropist.