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Use the step by step procedures: Social scientists have long been interested in the relationship between...

Use the step by step procedures: Social scientists have long been interested in the relationship between economic development and health. To gain some insight into this relationship, we can utilize data on the life expectancy of females from birth and GDP per capita. you’ll find data from 91 countries. Use the data in the sheet entitled “Part 2 Question 9” to calculate and interpret the correlation coefficient.

GNP	LExpF
600	75.5
2250	74.7
2980	77.7
2780	73.8
1690	75.7
1640	72.4
2242	74.0
1880	75.9
1320	74.8
2370	72.7
630	55.4
2680	67.6
1940	75.1
1260	69.2
980	67.6
330	66.1
1110	68.5
1160	66.5
2560	74.9
2560	72.8
2490	66.0
15540	76.8
26040	78.7
22080	77.7
19490	80.5
22320	78.4
5990	74.0
9550	76.7
16830	78.6
17320	79.9
23120	75.7
7600	72.4
11020	78.6
23660	80.0
34064	80.0
16100	77.9
17000	79.6
25430	81.8
20470	79.8
21790	78.3
168	42.0
6340	69.4
2490	55.0
3020	64.8
10920	77.4
1240	67.8
16150	75.4
5220	65.8
7050	65.2
1630	65.8
19860	72.9
210	56.0
380	70.9
14210	80.1
350	52.1
570	62.0
2320	71.6
110	62.5
170	48.1
380	59.2
730	66.1
11160	74.0
470	71.7
1420	68.9
2060	63.3
610	46.1
2040	59.7
1010	55.3
600	60.3
120	45.6
390	53.2
260	44.6
390	55.8
370	60.5
5310	62.6
200	41.2
960	62.5
80	48.1
1030	57.5
360	52.2
240	42.6
120	46.6
2530	63.5
480	51.0
810	49.5
1440	66.4
220	52.7
110	54.7
220	53.7
420	52.5
640	60.1

(1) Using a similar dataset in “Part 2 Question 10”, calculate and interpret the correlation coefficient for the data on a life expectancy of males from birth and GDP per capita.

GNP	LExpM
600	69.6
2250	68.3
2980	71.8
2780	65.4
1690	67.2
1640	66.5
2242	64.6
1880	66.4
1320	66.4
2370	65.5
630	51.0
2680	62.3
1940	68.1
1260	63.4
980	63.4
330	60.4
1110	64.4
1160	56.8
2560	68.4
2560	66.7
2490	62.1
15540	70.0
26040	70.7
22080	71.8
19490	72.3
22320	71.8
5990	65.4
9550	71.0
16830	72.0
17320	73.3
23120	67.2
7600	66.5
11020	72.5
23660	74.2
34064	73.9
16100	72.2
17000	73.3
25430	75.9
20470	73.0
21790	71.5
168	41.0
6340	66.8
2490	55.8
3020	63.0
10920	73.9
1240	64.2
16150	71.2
5220	62.2
7050	61.7
1630	62.5
19860	68.6
210	56.9
380	68.0
14210	74.3
350	52.5
570	58.5
2320	67.5
110	60.0
170	50.9
380	59.0
730	62.5
11160	68.7
470	67.8
1420	63.8
2060	61.6
610	42.9
2040	52.3
1010	50.1
600	57.8
120	42.4
390	49.9
260	41.4
390	52.2
370	56.5
5310	59.1
200	38.1
960	59.1
80	44.9
1030	55.0
360	48.8
240	39.4
120	43.4
2530	57.5
480	48.6
810	42.9
1440	64.9
220	49.9
110	51.3
220	50.3
420	50.4
640	56.5

Expert Solution

We use the formula :

For the first data set, we have :

	GNP (X)	LExpF (Y)	X*Y	X²	Y²
	600	75.5	45300	360000	5700.25
	2250	74.7	168075	5062500	5580.09
	2980	77.7	231546	8880400	6037.29
	2780	73.8	205164	7728400	5446.44
	1690	75.7	127933	2856100	5730.49
	1640	72.4	118736	2689600	5241.76
	2242	74	165908	5026564	5476
	1880	75.9	142692	3534400	5760.81
	1320	74.8	98736	1742400	5595.04
	2370	72.7	172299	5616900	5285.29
	630	55.4	34902	396900	3069.16
	2680	67.6	181168	7182400	4569.76
	1940	75.1	145694	3763600	5640.01
	1260	69.2	87192	1587600	4788.64
	980	67.6	66248	960400	4569.76
	330	66.1	21813	108900	4369.21
	1110	68.5	76035	1232100	4692.25
	1160	66.5	77140	1345600	4422.25
	2560	74.9	191744	6553600	5610.01
	2560	72.8	186368	6553600	5299.84
	2490	66	164340	6200100	4356
	15540	76.8	1193472	241491600	5898.24
	26040	78.7	2049348	678081600	6193.69
	22080	77.7	1715616	487526400	6037.29
	19490	80.5	1568945	379860100	6480.25
	22320	78.4	1749888	498182400	6146.56
	5990	74	443260	35880100	5476
	9550	76.7	732485	91202500	5882.89
	16830	78.6	1322838	283248900	6177.96
	17320	79.9	1383868	299982400	6384.01
	23120	75.7	1750184	534534400	5730.49
	7600	72.4	550240	57760000	5241.76
	11020	78.6	866172	121440400	6177.96
	23660	80	1892800	559795600	6400
	34064	80	2725120	1160356096	6400
	16100	77.9	1254190	259210000	6068.41
	17000	79.6	1353200	289000000	6336.16
	25430	81.8	2080174	646684900	6691.24
	20470	79.8	1633506	419020900	6368.04
	21790	78.3	1706157	474804100	6130.89
	168	42	7056	28224	1764
	6340	69.4	439996	40195600	4816.36
	2490	55	136950	6200100	3025
	3020	64.8	195696	9120400	4199.04
	10920	77.4	845208	119246400	5990.76
	1240	67.8	84072	1537600	4596.84
	16150	75.4	1217710	260822500	5685.16
	5220	65.8	343476	27248400	4329.64
	7050	65.2	459660	49702500	4251.04
	1630	65.8	107254	2656900	4329.64
	19860	72.9	1447794	394419600	5314.41
	210	56	11760	44100	3136
	380	70.9	26942	144400	5026.81
	14210	80.1	1138221	201924100	6416.01
	350	52.1	18235	122500	2714.41
	570	62	35340	324900	3844
	2320	71.6	166112	5382400	5126.56
	110	62.5	6875	12100	3906.25
	170	48.1	8177	28900	2313.61
	380	59.2	22496	144400	3504.64
	730	66.1	48253	532900	4369.21
	11160	74	825840	124545600	5476
	470	71.7	33699	220900	5140.89
	1420	68.9	97838	2016400	4747.21
	2060	63.3	130398	4243600	4006.89
	610	46.1	28121	372100	2125.21
	2040	59.7	121788	4161600	3564.09
	1010	55.3	55853	1020100	3058.09
	600	60.3	36180	360000	3636.09
	120	45.6	5472	14400	2079.36
	390	53.2	20748	152100	2830.24
	260	44.6	11596	67600	1989.16
	390	55.8	21762	152100	3113.64
	370	60.5	22385	136900	3660.25
	5310	62.6	332406	28196100	3918.76
	200	41.2	8240	40000	1697.44
	960	62.5	60000	921600	3906.25
	80	48.1	3848	6400	2313.61
	1030	57.5	59225	1060900	3306.25
	360	52.2	18792	129600	2724.84
	240	42.6	10224	57600	1814.76
	120	46.6	5592	14400	2171.56
	2530	63.5	160655	6400900	4032.25
	480	51	24480	230400	2601
	810	49.5	40095	656100	2450.25
	1440	66.4	95616	2073600	4408.96
	220	52.7	11594	48400	2777.29
	110	54.7	6017	12100	2992.09
	220	53.7	11814	48400	2883.69
	420	52.5	22050	176400	2756.25
	640	60.1	38464	409600	3612.01
Total	522454	6008.8	39768571	8895229284	407916

We obtain the following :

Using the above formula, we get Correlation coefficient r = 0.65

Correlation coefficient value of 0.65 indicates moderate positive linear relationship between life expectancy of females from birth and GDP per capita.

For the second data set, we have :

	GNP (X)	LExpM (Y)	X*Y	X²	Y²
	600	69.6	41760	360000	4844.16
	2250	68.3	153675	5062500	4664.89
	2980	71.8	213964	8880400	5155.24
	2780	65.4	181812	7728400	4277.16
	1690	67.2	113568	2856100	4515.84
	1640	66.5	109060	2689600	4422.25
	2242	64.6	144833.2	5026564	4173.16
	1880	66.4	124832	3534400	4408.96
	1320	66.4	87648	1742400	4408.96
	2370	65.5	155235	5616900	4290.25
	630	51	32130	396900	2601
	2680	62.3	166964	7182400	3881.29
	1940	68.1	132114	3763600	4637.61
	1260	63.4	79884	1587600	4019.56
	980	63.4	62132	960400	4019.56
	330	60.4	19932	108900	3648.16
	1110	64.4	71484	1232100	4147.36
	1160	56.8	65888	1345600	3226.24
	2560	68.4	175104	6553600	4678.56
	2560	66.7	170752	6553600	4448.89
	2490	62.1	154629	6200100	3856.41
	15540	70	1087800	241491600	4900
	26040	70.7	1841028	678081600	4998.49
	22080	71.8	1585344	487526400	5155.24
	19490	72.3	1409127	379860100	5227.29
	22320	71.8	1602576	498182400	5155.24
	5990	65.4	391746	35880100	4277.16
	9550	71	678050	91202500	5041
	16830	72	1211760	283248900	5184
	17320	73.3	1269556	299982400	5372.89
	23120	67.2	1553664	534534400	4515.84
	7600	66.5	505400	57760000	4422.25
	11020	72.5	798950	121440400	5256.25
	23660	74.2	1755572	559795600	5505.64
	34064	73.9	2517330	1160356096	5461.21
	16100	72.2	1162420	259210000	5212.84
	17000	73.3	1246100	289000000	5372.89
	25430	75.9	1930137	646684900	5760.81
	20470	73	1494310	419020900	5329
	21790	71.5	1557985	474804100	5112.25
	168	41	6888	28224	1681
	6340	66.8	423512	40195600	4462.24
	2490	55.8	138942	6200100	3113.64
	3020	63	190260	9120400	3969
	10920	73.9	806988	119246400	5461.21
	1240	64.2	79608	1537600	4121.64
	16150	71.2	1149880	260822500	5069.44
	5220	62.2	324684	27248400	3868.84
	7050	61.7	434985	49702500	3806.89
	1630	62.5	101875	2656900	3906.25
	19860	68.6	1362396	394419600	4705.96
	210	56.9	11949	44100	3237.61
	380	68	25840	144400	4624
	14210	74.3	1055803	201924100	5520.49
	350	52.5	18375	122500	2756.25
	570	58.5	33345	324900	3422.25
	2320	67.5	156600	5382400	4556.25
	110	60	6600	12100	3600
	170	50.9	8653	28900	2590.81
	380	59	22420	144400	3481
	730	62.5	45625	532900	3906.25
	11160	68.7	766692	124545600	4719.69
	470	67.8	31866	220900	4596.84
	1420	63.8	90596	2016400	4070.44
	2060	61.6	126896	4243600	3794.56
	610	42.9	26169	372100	1840.41
	2040	52.3	106692	4161600	2735.29
	1010	50.1	50601	1020100	2510.01
	600	57.8	34680	360000	3340.84
	120	42.4	5088	14400	1797.76
	390	49.9	19461	152100	2490.01
	260	41.4	10764	67600	1713.96
	390	52.2	20358	152100	2724.84
	370	56.5	20905	136900	3192.25
	5310	59.1	313821	28196100	3492.81
	200	38.1	7620	40000	1451.61
	960	59.1	56736	921600	3492.81
	80	44.9	3592	6400	2016.01
	1030	55	56650	1060900	3025
	360	48.8	17568	129600	2381.44
	240	39.4	9456	57600	1552.36
	120	43.4	5208	14400	1883.56
	2530	57.5	145475	6400900	3306.25
	480	48.6	23328	230400	2361.96
	810	42.9	34749	656100	1840.41
	1440	64.9	93456	2073600	4212.01
	220	49.9	10978	48400	2490.01
	110	51.3	5643	12100	2631.69
	220	50.3	11066	48400	2530.09
	420	50.4	21168	176400	2540.16
	640	56.5	36160	409600	3192.25
Total	522454	5585.7	36624925	8895229284	351374.2

We obtain the following :

Using the above formula, we get Correlation coefficient r = 0.643

Correlation coefficient value of 0.643 indicates moderate positive linear relationship between life expectancy of males from birth and GDP per capita.

milcah answered 1 year ago

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