Figure 4.2: Microsoft Excel output for simple linear regression SUMMARY OUTPUT Regression Statistics Multiple R 0.848766779 R Square 0.720405045 Adjusted R Square 0.717298435 Standard Error 0.008539025 Observations 92 ANOVA df SS MS F Significance F Regression 1 0.016908556 0.016908556 231.8942205 1.221326-26 Residual 90 0.006562346 Total 91 0.023470902 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 1.162999075 0.006559641 177.2961535 2.6688E-116 1.149967204 1.176030947 log(skinfold thickness) -0.063118994 0.00414491 -15.22807343 1.221326-26 -0.071353582 -0.054884407 Figure 4.3: Histogram of residuals Figure 4.4: Plot of residuals versus log(skin fold thickness)
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Step 1: The question asks to determine if a simple transformation of skin fold thickness can help to predict body density. Show more…
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SUMMARY OUTPUT Regression Statistics Multiple R 0.4543898 R Square 0.2064701 Adjusted R Square 0.1623851 Standard Error 1.4240469 Observations 20 ANOVA df SS MS F Significance F Regression 1 9.497625594 9.497626 4.683456 0.04414537 Residual 18 36.50237441 2.02791 Total 19 46 Coefficients Standard Error t Stat P-value Lower 95% Intercept 5.672082 0.835679513 6.787389 2.34E-06 3.916384472 Age -0.049988 0.023098205 -2.16413 0.044145 -0.098515031
Lien L.
SUMMARY OUTPUT Regression Statistics Multiple R 0.473932054 R Square 0.224611592 Adjusted R Square 0.218853757 Standard Error 14.85665558 Observations 408 ANOVA df SS MS F Significance F Regression 3 25830.70959 8610.236529 39.00973242 3.69997E-22 Residual 404 89170.96688 220.7202151 Total 407 115001.6765 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 385.4384477 338.9966744 1.136997725 0.25621316 -280.9792491 1051.856144 GDP Per Capita (Thousands) 0.28651666 0.046941033 6.103756974 2.4315E-09 0.194237479 0.37879584 Population (Millions) 0.041979674 0.00443387 9.467954334 2.42102E-19 0.033263338 0.050696011 Year -0.191084928 0.169402359 -1.127994491 0.259991678 -0.524105098 0.141935242 Table 1
Sri K.
SUMMARY OUTPUT Regression Statistics Multiple R 1 R Square 1 Adjusted R Square 65535 Standard Error 0 Observations 4 ANOVA df SS MS F Significance F Regression 3 19235.23924 6411.74641 #NUM! #NUM! Residual 0 0 65535 Total 3 19235.23924 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 1412.72036 0 65535 #NUM! 1412.72036 1412.72036 1412.72036 1412.72036 X Variable 1 -616.63372 0 65535 #NUM! -616.63372 -616.63372 -616.63372 -616.63372 X Variable 2 757.72152 0 65535 #NUM! 757.721529 757.721529 757.721529 757.721529 X Variable 3 -506.28783 0 65535 #NUM! -506.28783 -506.28783 -506.28783 -506.28783 RESIDUAL OUTPUT Observation Predicted Y Residuals Standard Residuals 1 1.653 -2.47358E-13 -0.6238259 2 3.677 3.20188E-13 0.80750171 3 167.6 5.40012E-13 1.36188915 4 19.39 1.27898E-13 0.32255269 PROBABILITY OUTPUT Percentile Y 12.5 1.653 37.5 3.677 62.5 19.39 87.5 167.6
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