Compute the correlation coefficient, r, for all five variables (columns). Interpret your findings whether you have determined any relationship between variables.
X1 X2 X3 X4 X5
The data (X1, X2, X3, X4, X5) are by city.
8 78 284 9.1 109 X1 =
death rate per 1000 residents
9.3 68 433 8.7 144 X2 = doctor availability per 100,000
residents
7.5 70 739 7.2 113 X3 =
hospital availability per 100,000 residents
8.9 96 1792 8.9 97 X4 = annual per capita
income in thousands of dollars
10.2 74 477 8.3 206 X5 =
population density people per square mile
8.3 111 362 10.9 124
8.8 77 671 10 152
8.8 168 636 9.1 162
10.7 82 329 8.7 150
11.7 89 634 7.6 134
8.5 149 631 10.8 292
8.3 60 257 9.5 108
8.2 96 284 8.8 111
7.9 83 603 9.5 182
10.3 130 686 8.7
129
7.4 145 345 11.2 158
9.6 112 1357 9.7
186
9.3 131 544 9.6 177
10.6 80 205 9.1 127
9.7 130 1264 9.2 179
11.6 140 688 8.3 80
8.1 154 354 8.4 103
9.8 118 1632 9.4 101
7.4 94 348 9.8 117
9.4 119 370 10.4 88
11.2 153 648 9.9 78
9.1 116 366 9.2 102
10.5 97 540 10.3 95
11.9 176 680 8.9 80
8.4 75 345 9.6 92
5 134 525 10.3 126
9.8 161 870 10.4
108
9.8 111 669 9.7 77
10.8 114 452 9.6 60
10.1 142 430 10.7 71
10.9 238 822 10.3 86
9.2 78 190 10.7 93
8.3 196 867 9.6 106
7.3 125 969 10.5
162
9.4 82 499 7.7 95
9.4 125 925 10.2 91
9.8 129 353 9.9 52
3.6 84 288 8.4 110
8.4 183 718 10.4 69
10.8 119 540 9.2 57
10.1 180 668 13 106
9 82 347 8.8 40
10 71 345 9.2 50
11.3 118 463 7.8 35
11.3 121 728 8.2 86
12.8 68 383 7.4 57
10 112 316 10.4 57
6.7 109 388 8.9 94
the correlation matrix for the variable is given as using ms-excel
X1 | X2 | X3 | X4 | X5 | |
X1 | 1 | ||||
X2 | 0.115765 | 1 | |||
X3 | 0.11059 | 0.295628 | 1 | ||
X4 | -0.17199 | 0.433288 | 0.027504 | 1 | |
X5 | -0.27761 | -0.01994 | 0.186616 | 0.128744 | 1 |
here sample size n=53 the significant value of r for sample size n=53 is 0.2706 at level of significance alpha=0.05
so r(X1,X5)=-0.2776, r(X2,X3)=0.2958 and , r(X2,X4) =0.4333 are significant
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