Question

1. Were there any strong relationships indicated?
2. Were there any extreme values that might skew results?
3. How would you use the regression equations generated by the software?
4. What preliminary conclusions would be supported and what further study indicated?

Response: Hemoglobin Model: carb_intake General Regression Analysis: Hemoglobin versus Carb_Intake Regression Equation Hemoglobin = 5.93337 + 0.00630756 Carb_Intake Coefficients Term Coef SE Coef T P Constant 5.93337 0.161506 36.7377 0.000 Carb_Intake 0.00631 0.000722 8.7397 0.000 Summary of Model S = 1.13003 R-Sq = 13.30% R-Sq(adj) = 13.12% PRESS = 641.917 R-Sq(pred) = 12.48% Analysis of Variance Source DF Seq SS Adj SS Adj MS F P Regression 1 97.537 97.537 97.5368 76.3822 0.0000000 Carb_Intake 1 97.537 97.537 97.5368 76.3822 0.0000000 Error 498 635.925 635.925 1.2770 Lack-of-Fit 223 336.136 336.136 1.5073 1.3827 0.0053349 Pure Error 275 299.789 299.789 1.0901 Total 499 733.462 Fits and Diagnostics for Unusual Observations Obs Hemoglobin Fit SE Fit Residual St Resid 14 12 8.55100 0.154608 3.44900 3.08111 R X 22 12 8.13470 0.110692 3.86530 3.43707 R 55 12 8.14101 0.111334 3.85899 3.43165 R 65 8 8.79069 0.180749 -0.79069 -0.70884 X 81 8 8.28609 0.126350 -0.28609 -0.25477 X 84 11 6.97411 0.061084 4.02589 3.56787 R 98 7 8.26716 0.124369 -1.26716 -1.12821 X 99 11 7.15072 0.052468 3.84928 3.41004 R 138 6 8.36808 0.135001 -2.36808 -2.11072 R X 142 10 7.52918 0.058365 2.47082 2.18944 R 152 10 6.84165 0.070719 3.15835 2.80042 R 161 11 7.42195 0.053296 3.57805 3.16987 R 192 10 6.86688 0.068730 3.13312 2.77775 R 213 7 8.31132 0.129001 -1.31132 -1.16807 X 223 12 7.78779 0.077524 4.21221 3.73634 R 237 11 7.18226 0.051615 3.81774 3.38198 R 241 10 7.12549 0.053316 2.87451 2.54659 R 243 11 7.98332 0.095609 3.01668 2.67917 R 278 10 7.26426 0.050549 2.73574 2.42338 R 285 8 8.64562 0.164877 -0.64562 -0.57751 X 301 9 8.29239 0.127012 0.70761 0.63018 X 321 12 7.59856 0.062714 4.40144 3.90100 R 334 9 8.35547 0.133664 0.64453 0.57440 X 356 10 7.29580 0.050598 2.70420 2.39545 R 368 12 8.10947 0.108131 3.89053 3.45874 R 375 11 7.66795 0.067718 3.33205 2.95396 R 385 11 7.47872 0.055701 3.52128 3.11990 R 435 10 7.62379 0.064465 2.37621 2.10622 R 460 10 7.38410 0.052083 2.61590 2.31736 R 499 10 7.20749 0.051106 2.79251 2.47372 R R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large leverage. Normplot of Residuals for Hemoglobin Residual Histogram for Hemoglobin

Answer 1

Ans 1 ) the value of R 2 =0.1330so r =0.3647 ,so there is not strong relationship between the variables .

Ans 2) yes there are extreme values that might skew results which are given below in results denoted by R .

Ans 3 ) the regression equations generated by the software is

Hemoglobin = 5.93337 + 0.00630756 Carb_Intake

Ans 4 ) Since the p value of F stat is less than 0.05 so we conclude that this model is significant and used for further analysis , also the p value of explanatory variable Carb intake  is also less than 0.05 so it is also significant and used for predicting the Hemoglobin for individuals.

Response: Hemoglobin Model: carb_intake General Regression Analysis: Hemoglobin versus Carb_Intake

Regression Equation

Hemoglobin = 5.93337 + 0.00630756 Carb_Intake

Coefficients

Term Coef SE Coef T P

Constant 5.93337 0.161506 36.7377 0.000

Carb_Intake 0.00631 0.000722 8.7397 0.000

Summary of Model

S = 1.13003 R-Sq = 13.30% R-Sq(adj) = 13.12% PRESS = 641.917 R-Sq(pred) = 12.48%

Analysis of Variance

Source DF Seq SS Adj SS Adj MS F P

Regression 1 97.537 97.537 97.5368 76.3822 0.0000000

Carb_Intake 1 97.537 97.537 97.5368 76.3822 0.0000000

Error 498 635.925 635.925 1.2770

Lack-of-Fit 223 336.136 336.136 1.5073 1.3827 0.0053349

Pure Error 275 299.789 299.789 1.0901 Total 499 733.462

Fits and Diagnostics for Unusual Observations Obs Hemoglobin Fit SE Fit Residual St Resid 14 12 8.55100 0.154608 3.44900 3.08111 R X 22 12 8.13470 0.110692 3.86530 3.43707 R 55 12 8.14101 0.111334 3.85899 3.43165 R 65 8 8.79069 0.180749 -0.79069 -0.70884 X 81 8 8.28609 0.126350 -0.28609 -0.25477 X 84 11 6.97411 0.061084 4.02589 3.56787 R 98 7 8.26716 0.124369 -1.26716 -1.12821 X 99 11 7.15072 0.052468 3.84928 3.41004 R 138 6 8.36808 0.135001 -2.36808 -2.11072 R X 142 10 7.52918 0.058365 2.47082 2.18944 R 152 10 6.84165 0.070719 3.15835 2.80042 R 161 11 7.42195 0.053296 3.57805 3.16987 R 192 10 6.86688 0.068730 3.13312 2.77775 R 213 7 8.31132 0.129001 -1.31132 -1.16807 X 223 12 7.78779 0.077524 4.21221 3.73634 R 237 11 7.18226 0.051615 3.81774 3.38198 R 241 10 7.12549 0.053316 2.87451 2.54659 R 243 11 7.98332 0.095609 3.01668 2.67917 R 278 10 7.26426 0.050549 2.73574 2.42338 R 285 8 8.64562 0.164877 -0.64562 -0.57751 X 301 9 8.29239 0.127012 0.70761 0.63018 X 321 12 7.59856 0.062714 4.40144 3.90100 R 334 9 8.35547 0.133664 0.64453 0.57440 X 356 10 7.29580 0.050598 2.70420 2.39545 R 368 12 8.10947 0.108131 3.89053 3.45874 R 375 11 7.66795 0.067718 3.33205 2.95396 R 385 11 7.47872 0.055701 3.52128 3.11990 R 435 10 7.62379 0.064465 2.37621 2.10622 R 460 10 7.38410 0.052083 2.61590 2.31736 R 499 10 7.20749 0.051106 2.79251 2.47372 R R denotes an observation with a large standardized residual. X denotes an observation whose X value gives it large leverage. Normplot of Residuals for Hemoglobin Residual Histogram for Hemoglobin