Question

In: Statistics and Probability

Solve Using R A.) Re-compute body fat percentage using the “Density” variable and Siri’s equation: (495/Density)...

Solve Using R

A.) Re-compute body fat percentage using the “Density” variable and Siri’s equation: (495/Density) – 450. Note that the values are percentages, so they must be between 0 and 100.

> Do you see any negative value? If so, change it to 0. Do you see any value >100? If so, change it to 100.

Are there any erroneous values in the variable “SiriBFPerc”? If so, employ your recomputed variable in further analyses. [Hint: the variable “SiriBFPerc” has only one decimal place. Before comparing it to your recomputed variable, you will need to round your recomputed variable. You can do so with the command round(variable,digits=1)].

Along with body fat percentage, consider the variables weight, height and abdomen circumference. Create a new dataset containing only the variables of interests. Produce numerical and graphical summaries for each of the selected variables, and a scatterplot matrix of them [Hint: use the command plot(new_dataset)].

> Are there any units (men) for which some of the measurements contain obvious mistakes? If so, remove those units in further analyses and re-produce summaries and plots.

> Do the distributions appear symmetric and bell-shaped, or are they skewed? Are there any very extreme values in any of the distributions?

B.) Compute the correlation between the body fat percentage and each of the variables weight, height and abdomen.

> What can you say about the relationship between the body fat percentage and each of the other three variables?

Fit a simple regression models for body fat percentage versus abdomen circumference. Make sure you provide: model employed, least square estimates of the parameters ?0, ?1 and ?2, the equation of the estimated regression line and the regression plot (i.e. scatter plot of Y vs X with the fitted regression line superimposed). [Hint: use functions lm, summary, plot and abline].

> What can you say about the regression? (Use language such as: the slope of the regression line represents [...], its estimated value= [...] can be interpreted by saying that [...], etc).

Consider the dataset contained in “BODY_FAT.TXT”. (BELOW)

Density	SiriBFperc	Over45	Weight	Height	NeckC	ChestC	AbdomenC	HipC	ThighC	KneeC	AnkleC	BicepsC	ForearmC	WristC
1.0708	12.3	0	154.25	67.75	36.2	93.1	85.2	94.5	59	37.3	21.9	32	27.4	17.1
1.0853	6.1	0	173.25	72.25	38.5	93.6	83	98.7	58.7	37.3	23.4	30.5	28.9	18.2
1.0414	25.3	0	154	66.25	34	95.8	87.9	99.2	59.6	38.9	24	28.8	25.2	16.6
1.0751	10.4	0	184.75	72.25	37.4	101.8	86.4	101.2	60.1	37.3	22.8	32.4	29.4	18.2
1.034	28.7	0	184.25	71.25	34.4	97.3	100	101.9	63.2	42.2	24	32.2	27.7	17.7
1.0502	20.9	0	210.25	74.75	39	104.5	94.4	107.8	66	42	25.6	35.7	30.6	18.8
1.0549	19.2	0	181	69.75	36.4	105.1	90.7	100.3	58.4	38.3	22.9	31.9	27.8	17.7
1.0704	12.4	0	176	72.5	37.8	99.6	88.5	97.1	60	39.4	23.2	30.5	29	18.8
1.09	4.1	0	191	74	38.1	100.9	82.5	99.9	62.9	38.3	23.8	35.9	31.1	18.2
1.0722	11.7	0	198.25	73.5	42.1	99.6	88.6	104.1	63.1	41.7	25	35.6	30	19.2
1.083	7.1	0	186.25	74.5	38.5	101.5	83.6	98.2	59.7	39.7	25.2	32.8	29.4	18.5
1.0812	7.8	0	216	76	39.4	103.6	90.9	107.7	66.2	39.2	25.9	37.2	30.2	19
1.0513	20.8	0	180.5	69.5	38.4	102	91.6	103.9	63.4	38.3	21.5	32.5	28.6	17.7
1.0505	21.2	0	205.25	71.25	39.4	104.1	101.8	108.6	66	41.5	23.7	36.9	31.6	18.8
1.0484	22.1	0	187.75	69.5	40.5	101.3	96.4	100.1	69	39	23.1	36.1	30.5	18.2
1.0512	20.9	0	162.75	66	36.4	99.1	92.8	99.2	63.1	38.7	21.7	31.1	26.4	16.9
1.0333	29	0	195.75	71	38.9	101.9	96.4	105.2	64.8	40.8	23.1	36.2	30.8	17.3
1.0468	22.9	0	209.25	71	42.1	107.6	97.5	107	66.9	40	24.4	38.2	31.6	19.3
1.0622	16	0	183.75	67.75	38	106.8	89.6	102.4	64.2	38.7	22.9	37.2	30.5	18.5
1.061	16.5	0	211.75	73.5	40	106.2	100.5	109	65.8	40.6	24	37.1	30.1	18.2
1.0551	19.1	0	179	68	39.1	103.3	95.9	104.9	63.5	38	22.1	32.5	30.3	18.4
1.064	15.2	0	200.5	69.75	41.3	111.4	98.8	104.8	63.4	40.6	24.6	33	32.8	19.9
1.0631	15.6	0	140.25	68.25	33.9	86	76.4	94.6	57.4	35.3	22.2	27.9	25.9	16.7
1.0584	17.7	0	148.75	70	35.5	86.7	80	93.4	54.9	36.2	22.1	29.8	26.7	17.1
1.0668	14	0	151.25	67.75	34.5	90.2	76.3	95.8	58.4	35.5	22.9	31.1	28	17.6
1.0911	3.7	0	159.25	71.5	35.7	89.6	79.7	96.5	55	36.7	22.5	29.9	28.2	17.7
1.0811	7.9	0	131.5	67.5	36.2	88.6	74.6	85.3	51.7	34.7	21.4	28.7	27	16.5
1.0468	22.9	0	148	67.5	38.8	97.4	88.7	94.7	57.5	36	21	29.2	26.6	17
1.091	3.7	0	133.25	64.75	36.4	93.5	73.9	88.5	50.1	34.5	21.3	30.5	27.9	17.2
1.079	8.8	0	160.75	69	36.7	97.4	83.5	98.7	58.9	35.3	22.6	30.1	26.7	17.6
1.0716	11.9	0	182	73.75	38.7	100.5	88.7	99.8	57.5	38.7	33.9	32.5	27.7	18.4
1.0862	5.7	0	160.25	71.25	37.3	93.5	84.5	100.6	58.5	38.8	21.5	30.1	26.4	17.9
1.0719	11.8	0	168	71.25	38.1	93	79.1	94.5	57.3	36.2	24.5	29	30	18.8
1.0502	21.3	0	218.5	71	39.8	111.7	100.5	108.3	67.1	44.2	25.2	37.5	31.5	18.7
1.0263	32.3	0	247.25	73.5	42.1	117	115.6	116.1	71.2	43.3	26.3	37.3	31.7	19.7
1.0101	40.1	1	191.75	65	38.4	118.5	113.1	113.8	61.9	38.3	21.9	32	29.8	17
1.0438	24.2	0	202.25	70	38.5	106.5	100.9	106.2	63.5	39.9	22.6	35.1	30.6	19
1.0346	28.4	1	196.75	68.25	42.1	105.6	98.8	104.8	66	41.5	24.7	33.2	30.5	19.4
1.0202	35.2	1	363.15	72.25	51.2	136.2	148.1	147.7	87.3	49.1	29.6	45	29	21.4
1.0258	32.6	1	203	67	40.2	114.8	108.1	102.5	61.3	41.1	24.7	34.1	31	18.3
1.0217	34.5	0	262.75	68.75	43.2	128.3	126.2	125.6	72.5	39.6	26.6	36.4	32.7	21.4
1.025	32.9	0	205	29.5	36.6	106	104.3	115.5	70.6	42.5	23.7	33.6	28.7	17.4
1.0279	31.6	1	217	70	37.3	113.3	111.2	114.1	67.7	40.9	25	36.7	29.8	18.4
1.0269	32	0	212	71.5	41.5	106.6	104.3	106	65	40.2	23	35.8	31.5	18.8
1.0814	7.7	0	125.25	68	31.5	85.1	76	88.2	50	34.7	21	26.1	23.1	16.1
1.067	13.9	0	164.25	73.25	35.7	96.6	81.5	97.2	58.4	38.2	23.4	29.7	27.4	18.3
1.0742	10.8	0	133.5	67.5	33.6	88.2	73.7	88.5	53.3	34.5	22.5	27.9	26.2	17.3
1.0665	5.6	0	148.5	71.25	34.6	89.8	79.5	92.7	52.7	37.5	21.9	28.8	26.8	17.9
1.0678	13.6	0	135.75	68.5	32.8	92.3	83.4	90.4	52	35.8	20.6	28.8	25.5	16.3
1.0903	4	1	127.5	66.75	34	83.4	70.4	87.2	50.6	34.4	21.9	26.8	25.8	16.8
1.0756	10.2	1	158.25	72.25	34.9	90.2	86.7	98.3	52.6	37.2	22.4	26	25.8	17.3
1.084	6.6	0	139.25	69	34.3	89.2	77.9	91	51.4	34.9	21	26.7	26.1	17.2
1.0807	8	1	137.25	67.75	36.5	89.7	82	89.1	49.3	33.7	21.4	29.6	26	16.9
1.0848	6.3	1	152.75	73.5	35.1	93.3	79.6	91.6	52.6	37.6	22.6	38.5	27.4	18.5
1.0906	3.9	0	136.25	67.5	37.8	87.6	77.6	88.6	51.9	34.9	22.5	27.7	27.5	18.5
1.0473	22.6	1	198	72	39.9	107.6	100	99.6	57.2	38	22	35.9	30.2	18.9
1.0524	20.4	1	181.5	68	39.1	100	99.8	102.5	62.1	39.6	22.5	33.1	28.3	18.5
1.0356	28	1	201.25	69.5	40.5	111.5	104.2	105.8	61.8	39.8	22.7	37.7	30.9	19.2
1.028	31.5	1	202.5	70.75	40.5	115.4	105.3	97	59.1	38	22.5	31.6	28.8	18.2
1.043	24.6	1	179.75	65.75	38.4	104.8	98.3	99.6	60.6	37.7	22.9	34.5	29.6	18.5
1.0396	26.1	1	216	73.25	41.4	112.3	104.8	103.1	61.6	40.9	23.1	36.2	31.8	20.2
1.0317	29.8	1	178.75	68.5	35.6	102.9	94.7	100.8	60.9	38	22.1	32.5	29.8	18.3
1.0298	30.7	1	193.25	70.25	38	107.6	102.4	99.4	61	39.4	23.6	32.7	29.9	19.1
1.0403	25.8	1	178	67	37.4	105.3	99.7	99.7	60.8	40.1	22.7	33.6	29	18.8
1.0264	32.3	1	205.5	70	40.1	105.3	105.5	108.3	65	41.2	24.7	35.3	31.1	18.4
1.0313	30	1	183.5	67.5	40.9	103	100.3	104.2	64.8	40.2	22.7	34.8	30.1	18.7
1.0499	21.5	1	151.5	70.75	35.6	90	83.9	93.9	55	36.1	21.7	29.6	27.4	17.4
1.0673	13.8	1	154.75	71.5	36.9	95.4	86.6	91.8	54.3	35.4	21.5	32.8	27.4	18.7
1.0847	6.3	1	155.25	69.25	37.5	89.3	78.4	96.1	56	37.4	22.4	32.6	28.1	18.1
1.0693	12.9	1	156.75	71.5	36.3	94.4	84.6	94.3	51.2	37.4	21.6	27.3	27.1	17.3
1.0439	24.3	1	167.5	71.5	35.5	97.6	91.5	98.5	56.6	38.6	22.4	31.5	27.3	18.6
1.0788	8.8	1	146.75	68.75	38.7	88.5	82.8	95.5	58.9	37.6	21.6	30.3	27.3	18.3
1.0796	8.5	1	160.75	73.75	36.4	93.6	82.9	96.3	52.9	37.5	23.1	29.7	27.3	18.2
1.068	13.5	1	125	64	33.2	87.7	76	88.6	50.9	35.4	19.1	29.3	25.7	16.9
1.072	11.8	1	143	65.75	36.5	93.4	83.3	93	55.5	35.2	20.9	29.4	27	16.8
1.0666	18.5	1	148.25	67.5	36	91.6	81.8	94.8	54.5	37	21.4	29.3	27	18.3
1.079	8.8	1	162.5	69.5	38.7	91.6	78.8	94.3	56.7	39.7	24.2	30.2	29.2	18.1
1.0483	22.2	1	177.75	68.5	38.7	102	95	98.3	55	38.3	21.8	30.8	25.7	18.8
1.0498	21.5	1	161.25	70.25	37.8	96.4	95.4	99.3	53.5	37.5	21.5	31.4	26.8	18.3
1.056	18.8	1	171.25	69.25	37.4	102.7	98.6	100.2	56.5	39.3	22.7	30.3	28.7	19
1.0283	31.4	1	163.75	67.75	38.4	97.7	95.8	97.1	54.8	38.2	23.7	29.4	27.2	19
1.0382	26.8	1	150.25	67.25	38.1	97.1	89	96.9	54.8	38	22	29.9	25.2	17.7
1.0568	18.4	1	190.25	72.75	39.3	103.1	97.8	99.6	58.9	39	23	34.3	29.6	19
1.0377	27	1	170.75	70	38.7	101.8	94.9	95	56	36.5	24.1	31.2	27.3	19.2
1.0378	27	1	168	69.25	38.5	101.4	99.8	96.2	56.3	36.6	22	29.7	26.3	18
1.0386	26.6	1	167	67.5	36.5	98.9	89.7	96.2	54.7	37.8	33.7	32.4	27.7	18.2
1.0648	14.9	1	157.75	67.25	37.7	97.5	88.1	96.9	57.2	37.7	21.8	32.6	28	18.8
1.0462	23.1	1	160	65.75	36.5	104.3	90.9	93.8	57.8	39.5	23.3	29.2	28.4	18.1
1.08	8.3	1	176.75	72.5	38	97.3	86	99.3	61	38.4	23.8	30.2	29.3	18.8
1.0666	14.1	1	176	73	36.7	96.7	86.5	98.3	60.4	39.9	24.4	28.8	29.6	18.7
1.052	20.5	1	177	70	37.2	99.7	95.6	102.2	58.3	38.2	22.5	29.1	27.7	17.7
1.0573	18.2	0	179.75	69.5	39.2	101.9	93.2	100.6	58.9	39.7	23.1	31.4	28.4	18.8
1.0795	8.5	1	165.25	70.5	37.5	97.2	83.1	95.4	56.9	38.3	22.1	30.1	28.2	18.4
1.0424	24.9	1	192.5	71.75	38	106.6	97.5	100.6	58.9	40.5	24.5	33.3	29.6	19.1
1.0785	9	1	184.25	74.5	37.3	99.6	88.8	101.4	57.4	39.6	24.6	30.3	27.9	17.8
1.0991	17.4	1	224.5	77.75	41.1	113.2	99.2	107.5	61.7	42.3	23.2	32.9	30.8	20.4
1.077	9.6	0	188.75	73.25	37.5	99.1	91.6	102.4	60.6	39.4	22.9	31.6	30.1	18.5
1.073	11.3	1	162.5	66.5	38.7	99.4	86.7	96.2	62.1	39.3	23.3	30.6	27.8	18.2
1.0582	17.8	1	156.5	68.25	35.9	95.1	88.2	92.8	54.7	37.3	21.9	31.6	27.5	18.2
1.0484	22.2	1	197	72	40	107.5	94	103.7	62.7	39	22.3	35.3	30.9	18.3
1.0506	21.2	1	198.5	73.5	40.1	106.5	95	101.7	59	39.4	22.3	32.2	31	18.6
1.0524	20.4	1	173.75	72	37	99.1	92	98.3	59.3	38.4	22.4	27.9	26.2	17
1.053	20.1	0	172.75	71.25	36.3	96.7	89.2	98.3	60	38.4	23.2	31	29.2	18.4
1.048	22.3	1	196.75	73.75	40.7	103.5	95.5	101.6	59.1	39.8	25.4	31	30.3	19.7
1.0412	25.4	0	177	69.25	39.6	104	98.6	99.5	59.5	36.1	22	30.1	27.2	17.7
1.0578	18	0	165.5	68.5	31.1	93.1	87.3	96.6	54.7	39	24.8	31	29.4	18.8
1.0547	19.3	0	200.25	73.5	38.6	105.2	102.8	103.6	61.2	39.3	23.5	30.5	28.5	18.1
1.0569	18.3	1	203.25	74.25	42	110	101.6	100.7	55.8	38.7	23.4	35.1	29.6	19.1
1.0593	17.3	0	194	75.5	38.5	110.1	88.7	102.1	57.5	40	24.8	35.1	30.7	19.2
1.05	21.4	0	168.5	69.25	34.2	97.8	92.3	100.6	57.5	36.8	22.8	32.1	26	17.3
1.0538	19.7	0	170.75	68.5	37.2	96.3	90.6	99.3	61.9	38	22.3	33.3	28.2	18.1
1.0355	28	0	183.25	70	37.1	108	105	103	63.7	40	23.6	33.5	27.8	17.4
1.0486	22.1	1	178.25	70	40.2	99.7	95	98.6	62.3	38.1	23.9	35.3	31.1	19.8
1.0503	21.3	0	163	70.25	35.3	93.5	89.6	99.8	61.5	37.8	21.9	30.7	27.6	17.4
1.0384	26.7	1	175.25	71.75	38	100.7	92.4	97.5	59.3	38.1	21.8	31.8	27.3	17.5
1.0607	16.7	0	158	69.25	36.3	97	86.6	92.6	55.9	36.3	22.1	29.8	26.3	17.3
1.0529	20.1	1	177.25	72.75	36.8	96	90	99.7	58.8	38.4	22.8	29.9	28	18.1
1.0671	13.9	1	179	72	41	99.2	90	96.4	56.8	38.8	23.3	33.4	29.8	19.5
1.0404	25.8	0	191	74	38.3	95.4	92.4	104.3	64.6	41.1	24.8	33.6	29.5	18.5
1.0575	18.1	0	187.5	72.25	38	101.8	87.5	101	58.5	39.2	24.5	32.1	28.6	18
1.0358	27.9	1	206.5	74.5	40.8	104.3	99.2	104.1	58.5	39.3	24.6	33.9	31.2	19.5
1.0414	25.3	0	185.25	71.5	39.5	99.2	98.1	101.4	57.1	40.5	23.2	33	29.6	18.4
1.0652	14.7	0	160.25	68.75	36.9	99.3	83.3	97.5	60.5	38.7	22.6	34.4	28	17.6
1.0623	16	1	151.5	66.75	36.9	94	86.1	95.2	58.1	36.5	22.1	30.6	27.5	17.6
1.0674	13.8	1	161	66.5	37.7	98.9	84.1	94	58.5	36.6	23.5	34.4	29.2	18
1.0587	17.5	1	167	67	36.6	101	89.9	100	60.7	36	21.9	35.6	30.2	17.6
1.0373	27.2	0	177.5	68.75	38.9	98.7	92.1	98.5	60.7	36.8	22.2	33.8	30.3	17.2
1.059	17.4	0	152.25	67.75	37.5	95.9	78	93.2	53.5	35.8	20.8	33.9	28.2	17.4
1.0515	20.8	0	192.25	73.25	39.8	103.9	93.5	99.5	61.7	39	21.8	33.3	29.6	18.1
1.0648	14.9	0	165.25	69.75	38.3	96.2	87	97.8	57.4	36.9	22.2	31.6	27.8	17.7
1.0575	18.1	1	171.75	71.5	35.5	97.8	90.1	95.8	57	38.7	23.2	27.5	26.5	17.6
1.0472	22.7	0	171.25	70.5	36.3	94.6	90.3	99.1	60.3	38.5	23	31.2	28.4	17.1
1.0452	23.6	1	197	73.25	37.8	103.6	99.8	103.2	61.2	38.1	22.6	33.5	28.6	17.9
1.0398	26.1	1	157	66.75	37.8	100.4	89.4	92.3	56.1	35.6	20.5	33.6	29.3	17.3
1.0435	24.4	0	168.25	69.5	36.5	98.4	87.2	98.4	56	36.9	23	34	29.8	18.1
1.0374	27.1	0	186	69.75	37.8	104.6	101.1	102.1	58.9	37.9	22.7	30.9	28.8	17.6
1.0491	21.8	0	166.75	70.75	37	92.9	86.1	95.6	58.8	36.1	22.4	32.7	28.3	17.1
1.0325	29.4	0	187.75	74	37.7	97.8	98.6	100.6	63.6	39.2	23.8	34.3	28.4	17.7
1.0481	22.4	0	168.25	71.25	34.3	98.3	88.5	98.3	58.1	38.4	22.5	31.7	27.4	17.6
1.0522	20.4	1	212.75	75	40.8	104.7	106.6	107.7	66.5	42.5	24.5	35.5	29.8	18.7
1.0422	24.9	0	176.75	71	37.4	98.6	93.1	101.6	59.1	39.6	21.6	30.8	27.9	16.6
1.0571	18.3	0	173.25	69.5	36.5	99.5	93	99.3	60.4	38.2	22	32	28.5	17.8
1.0459	23.3	1	167	67.75	37.5	102.7	91	98.9	57.1	36.7	22.3	31.6	27.5	17.9
1.0775	9.4	0	159.75	72.25	35.5	92.1	77.1	93.9	56.1	36.1	22.7	30.5	27.2	18.2
1.0754	10.3	0	188.15	77.5	38	96.6	85.3	102.5	59.1	37.6	23.2	31.8	29.7	18.3
1.0664	14.2	0	156	70.75	35.7	92.7	81.9	95.3	56.4	36.5	22	33.5	28.3	17.3
1.055	19.2	0	208.5	72.75	39.2	102	99.1	110.1	71.2	43.5	25.2	36.1	30.3	18.7
1.0322	29.6	0	206.5	69.75	40.9	110.9	100.5	106.2	68.4	40.8	24.6	33.3	29.7	18.4
1.0873	5.3	0	143.75	72.5	35.2	92.3	76.5	92.1	51.9	35.7	22	25.8	25.2	16.9
1.0416	25.2	0	223	70.25	40.6	114.1	106.8	113.9	67.6	42.7	24.7	36	30.4	18.4
1.0776	9.4	0	152.25	69	35.4	92.9	77.6	93.5	56.9	35.9	20.4	31.6	29	17.8
1.0542	19.6	0	241.75	74.5	41.8	108.3	102.9	114.4	72.9	43.5	25.1	38.5	33.8	19.6
1.0758	10.1	0	146	72.25	34.1	88.5	72.8	91.1	53.6	36.8	23.8	27.8	26.3	17.4
1.061	16.5	0	156.75	67.25	37.9	94	88.2	95.2	56.8	37.4	22.8	30.6	28.3	17.9
1.051	21	0	200.25	73.5	38.2	101.1	100.1	105	62.1	40	24.9	33.7	29.2	19.4
1.0594	17.3	0	171.5	75.25	35.6	92.1	83.5	98.3	57.3	37.8	21.7	32.2	27.7	17.7
1.0287	31.2	0	205.75	69	38.5	105.6	105	106.4	68.6	40	25.2	35.2	30.7	19.1
1.0761	10	0	182.5	72.25	37	98.5	90.8	102.5	60.8	38.5	25	31.6	28	18.6
1.0704	12.5	0	136.5	68.75	35.9	88.7	76.6	89.8	50.1	34.8	21.8	27	34.9	16.9
1.0477	22.5	0	177.25	71.5	36.2	101.1	92.4	99.3	59.4	39	24.6	30.1	28.2	18.2
1.0775	9.4	0	151.25	72.25	35	94	81.2	91.5	52.5	36.6	21	27	26.3	16.5
1.0653	14.6	0	196	73	38.5	103.8	95.6	105.1	61.4	40.6	25	31.3	29.2	19.1
1.069	13	0	184.25	68.75	40.7	98.9	92.1	103.5	64	37.3	23.5	33.5	30.6	19.7
1.0644	15.1	0	140	70.5	36	89.2	83.4	89.6	52.4	35.6	20.4	28.3	26.2	16.5
1.037	27.3	0	218.75	72	39.5	111.4	106	108.8	63.8	42	23.4	34	31.2	18.5
1.0549	19.2	0	217	73.75	40.5	107.5	95.1	104.5	64.8	41.3	25.6	36.4	33.7	19.4
1.0492	21.8	0	166.25	68	38.5	99.1	90.4	95.6	55.5	34.2	21.9	30.2	28.7	17.7
1.0525	20.3	0	224.75	72.25	43.9	108.2	100.4	106.8	63.3	41.7	24.6	37.2	33.1	19.8
1.018	34.3	0	228.25	69.5	40.4	114.9	115.9	111.9	74.4	40.6	24	36.1	31.8	18.8
1.061	16.5	0	172.75	69.5	37.6	99.1	90.8	98.1	60.1	39.1	23.4	32.5	29.8	17.4
1.0926	3	0	152.25	67.75	37	92.2	81.9	92.8	54.7	36.2	22.1	30.4	27.4	17.7
1.0983	0.7	0	125.75	65.5	34	90.8	75	89.2	50	34.8	22	24.8	25.9	16.9
1.0521	20.5	0	177.25	71	38.4	100.5	90.3	98.7	57.8	37.3	22.4	31	28.7	17.7
1.0603	16.9	0	176.25	71.5	38.7	98.2	90.3	99.9	59.2	37.7	21.5	32.4	28.4	17.8
1.0414	25.3	0	226.75	71.75	41.5	115.3	108.8	114.4	69.2	42.4	24	35.4	21	20.1
1.0763	9.9	0	145.25	69.25	36	96.8	79.4	89.2	50.3	34.8	22.2	31	26.9	16.9
1.0689	13.1	0	151	67	35.3	92.6	83.2	96.4	60	38.1	22	31.5	26.6	16.7
1.0316	29.9	0	241.25	71.5	42.1	119.2	110.3	113.9	69.8	42.6	24.8	34.4	29.5	18.4
1.0477	22.5	0	187.25	69.25	38	102.7	92.7	101.9	64.7	39.5	24.7	34.8	30.3	18.1
1.0603	16.9	0	234.75	74.5	42.8	109.5	104.5	109.9	69.5	43.1	25.8	39.1	32.5	19.9
1.0387	26.6	0	219.25	74.25	40	108.5	104.6	109.8	68.1	42.8	24.1	35.6	29	19
1.1089	0	0	118.5	68	33.8	79.3	69.4	85	47.2	33.5	20.2	27.7	24.6	16.5
1.0725	11.5	0	145.75	67.25	35.5	95.5	83.6	91.6	54.1	36.2	21.8	31.4	28.3	17.2
1.0713	12.1	0	159.25	69.75	35.3	92.3	86.8	96.1	58	39.4	22.7	30	26.4	17.4
1.0587	17.5	0	170.5	74.25	37.7	98.9	90.4	95.5	55.4	38.9	22.4	30.5	28.9	17.7
1.0794	8.6	0	167.5	71.5	39.4	89.5	83.7	98.1	57.3	39.7	22.6	32.9	29.3	18.2
1.0453	23.6	0	232.75	74.25	41.9	117.5	109.3	108.8	67.7	41.3	24.7	37.2	31.8	20
1.0524	20.4	0	210.5	72	38.5	107.4	98.9	104.1	63.5	39.8	23.5	36.4	30.4	19.1
1.052	20.5	0	202.25	72.5	40.8	109.2	98	101.8	62.8	41.3	24.8	36.6	32.4	18.8
1.0434	24.4	0	185	68.25	38	103.4	101.2	103.1	61.5	40.4	22.9	33.4	29.2	18.5
1.0728	11.4	0	153	69.25	36.4	91.4	80.6	92.3	54.3	36.3	21.8	29.6	27.3	17.9
1.014	38.1	0	244.25	76	41.8	115.2	113.7	112.4	68.5	45	25.5	37.1	31.2	19.9
1.0624	15.9	0	193.5	70.5	40.7	104.9	94.1	102.7	60.6	38.6	24.7	34	30.1	18.7
1.0429	24.7	0	224.75	74.75	38.5	106.7	105.7	111.8	65.3	43.3	26	33.7	29.9	18.5
1.047	22.8	0	162.75	72.75	35.4	92.2	85.6	96.5	60.2	38.9	22.4	31.7	27.1	17.1
1.0411	25.5	0	180	68.25	38.5	101.6	96.6	100.6	61.1	38.4	24.1	32.9	29.8	18.8
1.0488	22	0	156.25	69	35.5	97.8	86	96.2	57.7	38.6	24	31.2	27.3	17.4
1.0583	17.7	0	168	71.5	36.5	92	89.7	101	62.3	38	22.3	30.8	27.8	16.9
1.0841	6.6	0	167.25	72.75	37.6	94	78	99	57.5	40	22.5	30.6	30	18.5
1.0462	23.6	0	170.75	67.5	37.4	103.7	89.7	94.2	58.5	39	24.1	33.8	28.8	18.8
1.0709	12.2	0	178.25	70.25	37.8	102.7	89.2	99.2	60.2	39.2	23.8	31.7	28.4	18.6
1.0484	22.1	0	150	69.25	35.2	91.1	85.7	96.9	55.5	35.7	22	29.4	26.6	17.4
1.034	28.7	0	200.5	71.5	37.9	107.2	103.1	105.5	68.8	38.3	23.7	32.1	28.9	18.7
1.0854	6	0	184	74	37.9	100.8	89.1	102.6	60.6	39	24	32.9	29.2	18.4
1.0209	34.8	0	223	69.75	40.9	121.6	113.9	107.1	63.5	40.3	21.8	34.8	30.7	17.4
1.061	16.6	0	208.75	73	41.9	105.6	96.3	102	63.3	39.8	24.1	37.3	23.1	19.4
1.025	32.9	0	166	65.5	39.1	100.6	93.9	100.1	58.9	37.6	21.4	33.1	29.5	17.3
1.0254	32.8	1	195	72.5	40.2	102.7	101.3	101.7	60.7	39.4	23.3	36.7	31.6	18.4
1.0771	9.6	1	160.5	70.25	36	99.8	83.9	91.8	53	36.2	22.5	31.4	27.5	17.7
1.0742	10.8	1	159.75	70.75	34.5	92.9	84.4	94	56	38.2	22.6	29	26.2	17.6
1.0829	7.1	1	140.5	68	35.8	91.2	79.4	89	51.1	35	21.7	30.9	28.8	17.4
1.0373	27.2	1	216.25	74.5	40.2	115.6	104	109	63.7	40.3	23.2	36.8	31	18.9
1.0543	19.5	1	168.25	71.75	38.3	98.3	89.7	99.1	56.3	38.8	23	29.5	27.9	18.6
1.0561	18.7	1	194.75	70.75	39	103.7	97.6	104.2	60	40.9	25.5	32.7	30	19
1.0543	19.5	1	172.75	73	37.4	98.7	87.6	96.1	57.1	38.1	21.8	28.6	26.7	18
0.995	47.5	1	219	64	41.2	119.8	122.1	112.8	62.5	36.9	23.6	34.7	29.1	18.4
1.0678	13.6	1	149.25	69.75	34.8	92.8	81.1	96.3	53.8	36.5	21.5	31.3	26.3	17.8
1.0819	7.5	1	154.5	70	36.9	93.3	81.5	94.4	54.7	39	22.6	27.5	25.9	18.6
1.0433	24.5	1	199.25	71.75	39.4	106.8	100	105	63.9	39.2	22.9	35.7	30.4	19.2
1.0646	15	1	154.5	69.25	37.6	93.9	88.7	94.5	53.7	36.2	22	28.5	25.7	17.1
1.0706	12.4	1	153.25	70.5	38.5	99	91.8	96.2	57.7	38.1	23.9	31.4	29.9	18.9
1.0399	26	1	230	72.25	42.5	119.9	110.4	105.5	64.2	42.7	27	38.4	32	19.6
1.0726	11.5	1	161.75	67.5	37.4	94.2	87.6	95.6	59.7	40.2	23.4	27.9	27	17.8
1.0874	5.2	1	142.25	67.25	35.2	92.7	82.8	91.9	54.4	35.2	22.5	29.4	26.8	17
1.074	10.9	1	179.75	68.75	41.1	106.9	95.3	98.2	57.4	37.1	21.8	34.1	31.1	19.2
1.0703	12.5	1	126.5	66.75	33.4	88.8	78.2	87.5	50.8	33	19.7	25.3	22	15.8
1.065	14.8	1	169.5	68.25	37.2	101.7	91.1	97.1	56.6	38.5	22.6	33.4	29.3	18.8
1.0418	25.2	1	198.5	74.25	38.3	105.3	96.7	106.6	64	42.6	23.4	33.2	30	18.4
1.0647	14.9	1	174.5	69.5	38.1	104	89.4	98.4	58.4	37.4	22.5	34.6	30.1	18.8
1.0601	17	1	167.75	68.5	37.4	98.6	93	97	55.4	38.8	23.2	32.4	29.7	19
1.0745	10.6	1	147.75	65.75	35.2	99.6	86.4	90.1	53	35	21.3	31.7	27.3	16.9
1.062	16.1	1	182.25	71.75	39.4	103.4	96.7	100.7	59.3	38.6	22.8	31.8	29.1	19
1.0636	15.4	1	175.5	71.5	38	100.2	88.1	97.8	57.1	38.9	23.6	30.9	29.6	18
1.0384	26.7	1	161.75	67.25	35.1	94.9	94.9	100.2	56.8	35.9	21	27.8	26.1	17.6
1.0403	25.8	1	157.75	67.5	40.4	97.2	93.3	94	54.3	35.7	21	31.3	28.7	18.3
1.0563	18.6	1	168.75	67.5	38.3	104.7	95.6	93.7	54.4	37.1	22.7	30.3	26.3	18.3
1.0424	24.8	1	191.5	72.25	40.6	104	98.2	101.1	59.3	40.3	23	32.6	28.5	19
1.0372	27.3	1	219.15	69.5	40.2	117.6	113.8	111.8	63.4	41.1	22.3	35.1	29.6	18.5
1.0705	12.4	1	155.25	69.5	37.9	95.8	82.8	94.5	61.2	39.1	22.3	29.8	28.9	18.3
1.0316	29.9	1	189.75	65.75	40.8	106.4	100.5	100.5	59.2	38.1	24	35.9	30.5	19.1
1.0599	17	1	127.5	65.75	34.7	93	79.7	87.6	50.7	33.4	20.1	28.5	24.8	16.5
1.0207	35	1	224.5	68.25	38.8	119.6	118	114.3	61.3	42.1	23.4	34.9	30.1	19.4
1.0304	30.4	1	234.25	72	41.4	119.7	109	109.1	63.7	42.4	24.6	35.6	30.7	19.5
1.0256	32.6	1	227.75	72.75	41.3	115.8	113.4	109.8	65.6	46	25.4	35.3	29.8	19.5
1.0334	29	1	199.5	68.5	40.7	118.3	106.1	101.6	58.2	38.8	24.1	32.1	29.3	18.5
1.0641	15.2	1	155.5	69.25	36.3	97.4	84.3	94.4	54.3	37.5	22.6	29.2	27.3	18.5
1.0308	30.2	1	215.5	70.5	40.8	113.7	107.6	110	63.3	44	22.6	37.5	32.6	18.8
1.0736	11	1	134.25	67	34.9	89.2	83.6	88.8	49.6	34.8	21.5	25.6	25.7	18.5
1.0236	33.6	1	201	69.75	40.9	108.5	105	104.5	59.6	40.8	23.2	35.2	28.6	20.1
1.0328	29.3	1	186.75	66	38.9	111.1	111.5	101.7	60.3	37.3	21.5	31.3	27.2	18
1.0399	26	1	190.75	70.5	38.9	108.3	101.3	97.8	56	41.6	22.7	30.5	29.4	19.8
1.0271	31.9	1	207.5	70	40.8	112.4	108.5	107.1	59.3	42.2	24.6	33.7	30	20.9

Expert Solution

Loading the dataset

# make sure .csv file is in your working directory
bodyfat <- read.csv("bodyfat.csv")
head(bodyfat)

##   Density bodyfat Age Weight Height Neck Chest Abdomen   Hip Thigh Knee
## 1  1.0708    12.3  23 154.25  67.75 36.2  93.1    85.2  94.5  59.0 37.3
## 2  1.0853     6.1  22 173.25  72.25 38.5  93.6    83.0  98.7  58.7 37.3
## 3  1.0414    25.3  22 154.00  66.25 34.0  95.8    87.9  99.2  59.6 38.9
## 4  1.0751    10.4  26 184.75  72.25 37.4 101.8    86.4 101.2  60.1 37.3
## 5  1.0340    28.7  24 184.25  71.25 34.4  97.3   100.0 101.9  63.2 42.2
## 6  1.0502    20.9  24 210.25  74.75 39.0 104.5    94.4 107.8  66.0 42.0
##   Ankle Biceps Forearm Wrist
## 1  21.9   32.0    27.4  17.1
## 2  23.4   30.5    28.9  18.2
## 3  24.0   28.8    25.2  16.6
## 4  22.8   32.4    29.4  18.2
## 5  24.0   32.2    27.7  17.7
## 6  25.6   35.7    30.6  18.8

names(bodyfat)

##  [1] "Density" "bodyfat" "Age"     "Weight"  "Height"  "Neck"    "Chest"  
##  [8] "Abdomen" "Hip"     "Thigh"   "Knee"    "Ankle"   "Biceps"  "Forearm"
## [15] "Wrist"

orchestra answered 1 year ago

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1)Using R, construct one plot of the density function for a uniformly distributed continuous random variable...

1)Using R, construct one plot of the density function for a uniformly distributed continuous random variable defined between 0 and 6. Make sure you include a main title, label both axis correctly and include a legend in your figure. The main title needs to include your last name, also include your R code with your answer. 2) Using R, construct one plot of the density function for a Chi-square distributed random variable. The plots should contain six lines corresponding to...

Write the equation of the line. What is r? What is r squared? Using the equation...

Write the equation of the line. What is r? What is r squared? Using the equation of the line if x is 25 what is y? Using the equation of the line if y is 20 what is x. x 25 32 27 24 26 18 20 23 20 16 19 15 20 27 27 y 28 34 36 28 31 22 24 26 24 23 22 13 23 35 29

Please solve it by R (1) Find the mean and variance of the variable of ’volume’...

Please solve it by R (1) Find the mean and variance of the variable of ’volume’ in ’lung’ dataset in package ’ISwR’. (2) Check the normality of the variable of ’volume’ in ’lung’ dataset in package ’ISwR’ with significance level α = 0.1. (3) Test if the mean of ’volume’ is less than 3.3 with significance level α = 0.05.

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A....

Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation, A. dy/dx = y(xy^6 - 1) B. x dy/dx + y = 1/y^2 C. t^2 dy/dt + y^2 = ty