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AUO_MAT111_M3A2_TestingforCorrelationbyLinearRegression3.xls
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Study 1

Brain Weight Body Weight
3.385 44.5
0.48 15.5
1.35 8.1
465 423
36.33 119.5
27.66 115
14.83 98.2
1.04 5.5
4.19 58
0.425 6.4
0.101 4
0.92 5.7
1 6.6 SUMMARY OUTPUT
0.005 0.14
0.06 1 Regression Statistics
3.5 10.8 Multiple R 0.9341638423 Correlation Coefficient
2 12.3 R Square 0.8726620843 0.934
1.7 6.3 Adjusted R Square 0.8705397857
2547 4603 Standard Error 334.7197597868
0.023 0.3 Observations 62
187.1 419
521 655 ANOVA
0.785 3.5 df SS MS F Significance F
10 115 Regression 1 46068314.4790047 46068314.4790047 411.1872318014 1.54293494466785E-28
3.3 25.6 Residual 60 6722239.05550498 112037.31759175
0.2 5 Total 61 52790553.5345097
1.41 17.5
529 680 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
207 406 Intercept 91.0043962074 43.5525814971 2.0895293248 0.0409081847 3.8862622957 178.1225301192 3.8862622957 178.1225301192
85 325 Brain Weight 0.9664963677 0.0476628948 20.2777521388 1.54293494466792E-28 0.8711563829 1.0618363524 0.8711563829 1.0618363524
0.75 12.3
62 1320
6654 5712
3.5 3.9
6.8 179
35 56
4.05 17
0.12 1
0.023 0.4
0.01 0.25
1.4 12.5
250 490
2.5 12.1
55.5 175
100 157
52.16 440
10.55 179.5
0.55 2.4
60 81
3.6 21
4.288 39.2
0.28 1.9
0.075 1.2
0.122 3
0.048 0.33
192 180
3 25
160 169
0.9 2.6
1.62 11.4
0.104 2.5
4.235 50.4
Question: Is there a correlation between brain weight and body weight across mammalian species?
References: Spaeth, H. (1991). Mathematical algorithms for linear regression. New York, NY: Academic Press. Weisberg, S. (1980). Applied linear regression. New York, NY: John Wiley & Sons.

Study 1
Body Weight

Study 2

Water Temperature Length of Fish
25 620
25 1315
25 2120
25 2600
25 3110 SUMMARY OUTPUT
25 3535
25 3935 Regression Statistics
25 4465 Multiple R 0.1811179714 Correlation Coefficient
25 4530 R Square 0.0328037196 0.181
25 4570 Adjusted R Square 0.0097752367
25 4600 Standard Error 1322.4514677795
27 625 Observations 44
27 1215
27 2110 ANOVA
27 2805 df SS MS F Significance F
27 3255 Regression 1 2491249.64090912 2491249.64090912 1.4244846154 0.2393648768
27 4015 Residual 42 73452871.1545454 1748877.88463203
27 4315 Total 43 75944120.7954545
27 4495
27 4535 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
27 4600 Intercept 6087.0136363636 2504.4185053391 2.4305097664 0.0194286831 1032.8924745389 11141.1347981884 1032.8924745389 11141.1347981884
27 4600 Water Temperature -106.4136363636 89.1596597691 -1.1935177483 0.2393648768 -286.3451143732 73.5178416459 -286.3451143732 73.5178416459
29 590
29 1305
29 2140
29 2890
29 3920
29 3920
29 4515
29 4520
29 4525
29 4565
29 4566
31 590
31 1205
31 1915
31 2140
31 2710
31 3020
31 3030
31 3040
31 3180
31 3257
31 3214
Question: Is there a correlation between water temperature and the length that fish grow to?

Study 2
Length of Fish

Study 3

Age Systolic Blood Pressure
39 144
47 220
45 138
47 145
65 162
46 142
67 170
42 124
67 158
56 154
64 162
56 150
59 140 SUMMARY OUTPUT
34 110
42 128 Regression Statistics
48 130 Multiple R 0.6575672832 Correlation Coefficient
45 135 R Square 0.4323947319 0.658
17 114 Adjusted R Square 0.4121231152
20 116 Standard Error 17.3137476151
19 124 Observations 30
36 136
50 142 ANOVA
39 120 df SS MS F Significance F
21 120 Regression 1 6394.0226852216 6394.0226852216 21.3300565992 0.0000786726
44 160 Residual 28 8393.4439814451 299.7658564802
53 158 Total 29 14787.4666666667
63 144
29 130 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
25 125 Intercept 98.7147181382 10.0004675622 9.8710102827 0.0000000001 78.2296889626 119.1997473138 78.2296889626 119.1997473138
69 175 Age 0.9708703514 0.2102157419 4.618447423 0.0000786726 0.5402629244 1.4014777785 0.5402629244 1.4014777785
Question: Is there a correlation between age and systolic blood pressure?

Study 3
Systolic Blood Pressure

Example

Chirps/Second Temperature (F)
20 88.6
16 71.6
19.8 93.3
18.4 84.3
17.1 80.6
15.5 75.2
14.7 69.7
15.7 71.6
15.4 69.4
16.3 83.3
15 79.6
17.2 82.6
16 80.6
17 83.5
14.4 76.3
Question: Is there a correlation between the number of times a cricket chirps per second and air temperature?

Example