Regression Analysis

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econ_217_final_assignment_output.xlsx
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Sheet1

X1 X2 X3 X4 X5 X6 SUMMARY OUTPUT
8 78 284 9.100000381 109 1
9.300000191 68 433 8.699999809 144 1 Regression Statistics
7.5 70 739 7.199999809 113 0 Multiple R 0.384879494
8.899999619 96 1792 8.899999619 97 1 R Square 0.1481322249
10.19999981 74 477 8.300000191 206 0 Adjusted R Square 0.0575079935
8.300000191 111 362 10.89999962 124 1 Standard Error 1.6140177921
8.800000191 77 671 10 152 0 Observations 53
8.800000191 168 636 9.100000381 162 1
10.69999981 82 329 8.699999809 150 0 ANOVA
11.69999981 89 634 7.599999905 134 1 df SS MS F Significance F
8.5 149 631 10.80000019 292 0 Regression 5 21.2907935985 4.2581587197 1.634576345 0.1693984529
8.300000191 60 257 9.5 108 0 Residual 47 122.4375113663 2.6050534333
8.199999809 96 284 8.800000191 111 1 Total 52 143.7283049648
7.900000095 83 603 9.5 182 0
10.30000019 130 686 8.699999809 129 0 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
7.400000095 145 345 11.19999981 158 0 Intercept 12.4472698005 2.0689081316 6.0163472753 0.0000002543 8.2851634929 16.6093761081 8.2851634929 16.6093761081
9.600000381 112 1357 9.699999809 186 1 X2 0.0068590416 0.0070714457 0.9699631303 0.3370302141 -0.0073668722 0.0210849554 -0.0073668722 0.0210849554
9.300000191 131 544 9.600000381 177 0 X3 0.0006953017 0.0007618778 0.9126157311 0.3661023488 -0.0008373988 0.0022280022 -0.0008373988 0.0022280022
10.60000038 80 205 9.100000381 127 0 X4 -0.3364059981 0.2367500727 -1.4209330299 0.16193722 -0.8126857109 0.1398737147 -0.8126857109 0.1398737147
9.699999809 130 1264 9.199999809 179 1 X5 -0.0096878132 0.0049467179 -1.9584325001 0.0561288542 -0.0196393261 0.0002636997 -0.0196393261 0.0002636997
11.60000038 140 688 8.300000191 80 0 X6 -0.2342639646 0.4739425474 -0.494287685 0.6234054778 -1.1877133883 0.7191854592 -1.1877133883 0.7191854592
8.100000381 154 354 8.399999619 103 0
9.800000191 118 1632 9.399999619 101 1 PREDICTION Ex1
7.400000095 94 348 9.800000191 117 0 X2 121
9.399999619 119 370 10.39999962 88 1 X3 480
11.19999981 153 648 9.899999619 78 0 X4 9.8
9.100000381 116 366 9.199999809 102 1 X5 110
10.5 97 540 10.30000019 95 0 X6 0
11.89999962 176 680 8.899999619 80 0 predictive X1 9.2485204228 21*J
8.399999619 75 345 9.600000381 92 1 Model to use is:X1= 12.4472698+0.006859042*X2 + 0.00695302* X3 + -0.336405998*X4 + -0.009687813 *X5 +-0.23263965 *X6.
5 134 525 10.30000019 126 0
9.800000191 161 870 10.39999962 108 0
9.800000191 111 669 9.699999809 77 1
10.80000019 114 452 9.600000381 60 0
10.10000038 142 430 10.69999981 71 0
10.89999962 238 822 10.30000019 86 1
9.199999809 78 190 10.69999981 93 0
8.300000191 196 867 9.600000381 106 0
7.300000191 125 969 10.5 162 1
9.399999619 82 499 7.699999809 95 1
9.399999619 125 925 10.19999981 91 1
9.800000191 129 353 9.899999619 52 1
3.599999905 84 288 8.399999619 110 1
8.399999619 183 718 10.39999962 69 0
10.80000019 119 540 9.199999809 57 0
10.10000038 180 668 13 106 0
9 82 347 8.800000191 40 0
10 71 345 9.199999809 50 0
11.30000019 118 463 7.800000191 35 0
11.30000019 121 728 8.199999809 86 1
12.80000019 68 383 7.400000095 57 1
10 112 316 10.39999962 57 1
6.699999809 109 388 8.899999619 94 0
The data (X1, X2, X3, X4, X5) are by city.
X1 = death rate per 1000 residents
X2 = doctor availability per 100,000 residents
X3 = hospital availability per 100,000 residents
X4 = annual per capita income in thousands of dollars
X5 = population density people per square mile
Reference: Life In America's Small Cities, by G.S. Thomas
X6=gender where 0-male and 1-female

Sheet2

SUMMARY OUTPUT OUTPUT (X1 AND X2)
Regression Statistics
Multiple R 0.1157650383
R Square 0.0134015441
Adjusted R Square -0.0059435237
Standard Error 1.6674632826
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 1.9261812179 1.9261812179 0.6927628411 0.4091068387
Residual 51 141.8021237468 2.780433799
Total 52 143.7283049648
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 8.7159045495 0.7446650344 11.7044632778 4.61410013658965E-16 7.2209271121 10.2108819869 7.2209271121 10.2108819869
X2 0.0050799708 0.0061033592 0.8323237598 0.4091068387 -0.0071730339 0.0173329756 -0.0071730339 0.0173329756

Sheet3

SUMMARY OUTPUT OUTPUT (X1 AND X3)
Regression Statistics
Multiple R 0.1105901915
R Square 0.0122301905
Adjusted R Square -0.007137845
Standard Error 1.6684528493
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 1.7578245446 1.7578245446 0.6314626217 0.4305018113
Residual 51 141.9704804202 2.7837349102
Total 52 143.7283049648
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 8.9796442292 0.4699375903 19.1081633279 6.70185229455272E-25 8.0362051499 9.9230833086 8.0362051499 9.9230833086
X3 0.0005527642 0.0006956105 0.7946462243 0.4305018113 -0.0008437321 0.0019492606 -0.0008437321 0.0019492606

Sheet4

SUMMARY OUTPUT (X1 AND X4)
Regression Statistics
Multiple R 0.1719923933
R Square 0.0295813833
Adjusted R Square 0.0105535673
Standard Error 1.6537338791
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 4.2516820855 4.2516820855 1.55463892 0.2181480061
Residual 51 139.4766228793 2.7348357427
Total 52 143.7283049648
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 11.81449977 2.0249212427 5.8345477941 0.0000003721 7.749300747 15.8796987931 7.749300747 15.8796987931
X4 -0.2658837973 0.2132441396 -1.246851603 0.2181480061 -0.693989271 0.1622216764 -0.693989271 0.1622216764

Sheet5

SUMMARY OUTPUT (X1 AND X5)
Regression Statistics
Multiple R 0.2776069569
R Square 0.0770656225
Adjusted R Square 0.05896887
Standard Error 1.6127664314
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 11.0765112926 11.0765112926 4.2585332643 0.0441603009
Residual 51 132.6517936722 2.6010155622
Total 52 143.7283049648
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 10.3879973658 0.5693500788 18.2453603736 5.26510049987318E-24 9.244979388 11.5310153435 9.244979388 11.5310153435
X5 -0.009782377 0.0047403933 -2.0636213956 0.0441603009 -0.0192991136 -0.0002656404 -0.0192991136 -0.0002656404

Sheet6

SUMMARY OUTPUT(X1 AND X6)
Regression Statistics
Multiple R 0.012856848
R Square 0.0001652985
Adjusted R Square -0.0194393034
Standard Error 1.6786113944
Observations 53
ANOVA
df SS MS F Significance F
Regression 1 0.0237580792 0.0237580792 0.0084316193 0.9271977303
Residual 51 143.7045468856 2.8177362134
Total 52 143.7283049648
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 9.3242555434 0.3068788542 30.3841578376 2.45356024945699E-34 8.7081705362 9.9403405506 8.7081705362 9.9403405506
X6 -0.0427752642 0.4658404583 -0.0918238496 0.9271977303 -0.9779890077 0.8924384794 -0.9779890077 0.8924384794

Sheet7

SUMMARY OUTPUT(X1,X2,X3,X4,X5)
Regression Statistics
Multiple R 0.384879494
R Square 0.1481322249
Adjusted R Square 0.0575079935
Standard Error 1.6140177921
Observations 53
ANOVA
df SS MS F Significance F
Regression 5 21.2907935985 4.2581587197 1.634576345 0.1693984529
Residual 47 122.4375113663 2.6050534333
Total 52 143.7283049648
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 12.4472698005 2.0689081316 6.0163472753 0.0000002543 8.2851634929 16.6093761081 8.2851634929 16.6093761081
X2 0.0068590416 0.0070714457 0.9699631303 0.3370302141 -0.0073668722 0.0210849554 -0.0073668722 0.0210849554
X3 0.0006953017 0.0007618778 0.9126157311 0.3661023488 -0.0008373988 0.0022280022 -0.0008373988 0.0022280022
X4 -0.3364059981 0.2367500727 -1.4209330299 0.16193722 -0.8126857109 0.1398737147 -0.8126857109 0.1398737147
X5 -0.0096878132 0.0049467179 -1.9584325001 0.0561288542 -0.0196393261 0.0002636997 -0.0196393261 0.0002636997
X6 -0.2342639646 0.4739425474 -0.494287685 0.6234054778 -1.1877133883 0.7191854592 -1.1877133883 0.7191854592