Question

this is a four part question and I am lost: the question is at the top and the data follows:

1. Think about it:
   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?

a.            Response: Hemoglobin Model: Glucoseb.           

General Regression Analysis: Hemoglobin versus Glucose

Regression Equation

Hemoglobin = 4.44742 + 0.0241019 Glucose

Coefficients

Term         Coef   SE Coef        T      P

Constant 4.44742 0.124943 35.5957 0.000

Glucose   0.02410 0.001017 23.6982 0.000

Summary of Model

S = 0.831988     R-Sq = 53.00%        R-Sq(adj) = 52.91%

PRESS = 348.310 R-Sq(pred) = 52.51%

Analysis of Variance

Source          DF   Seq SS   Adj SS   Adj MS        F          P

Regression       1 388.744 388.744 388.744 561.603 0.0000000

Glucose        1 388.744 388.744 388.744 561.603 0.0000000

Error          498 344.718 344.718    0.692

Lack-of-Fit 135 167.864 167.864    1.243    2.552 0.0000000

Pure Error   363 176.854 176.854    0.487

Total          499 733.462

Fits and Diagnostics for Unusual Observations

Obs Hemoglobin      Fit    SE Fit Residual St Resid

14          12 10.0150 0.121499   1.98503   2.41175 R X

17           6   7.7976 0.043273 -1.79759 -2.16352 R

22          12   9.6775 0.108033   2.32246   2.81529 R X

55          12   9.3883 0.096666   2.61168   3.16049 R X

74           6   7.7735 0.042763 -1.77349 -2.13445 R

84          11   9.5088 0.101378   1.49117   1.80576     X

88           6   7.8699 0.044908 -1.86990 -2.25078 R

99          11   8.3278 0.057982   2.67217   3.21961 R

133           6   7.7976 0.043273 -1.79759 -2.16352 R

138           6   7.8217 0.043801 -1.82169 -2.19261 R

142          10   8.1109 0.051299   1.88909   2.27490 R

152          10   7.9904 0.047940   2.00959   2.41943 R

159           6   7.8940 0.045485 -1.89400 -2.27988 R

161          11   8.5447 0.065267   2.45525   2.96019 R

165          6   7.8699 0.044908 -1.86990 -2.25078 R

173           6   7.7012 0.041344 -1.70118 -2.04725 R

189           6   7.8217 0.043801 -1.82169 -2.19261 R

192          10   9.7739 0.111861   0.22605   0.27419     X

202          10   8.0145 0.048588   1.98549   2.39052 R

218          10   8.1109 0.051299   1.88909   2.27490 R

223          12   9.7739 0.111861   2.22605   2.70010 R X

229           6   7.8458 0.044346 -1.84579 -2.22169 R

237          11   9.2196 0.090137   1.78040   2.15260 R

241          10   8.2073 0.054180   1.79268   2.15927 R

243          11   9.2196 0.090137   1.78040   2.15260 R

278          10   8.0627 0.049921   1.93729   2.33271 R

282           6   7.8458 0.044346 -1.84579 -2.22169 R

312           6   7.7012 0.041344 -1.70118 -2.04725 R

321          12 12.1600 0.209508 -0.16004 -0.19876     X

368          12   9.5811 0.104223   2.41887   2.93042 R X

375          11   8.9786 0.080983   2.02142   2.44121 R

385          11 10.1837 0.128295   0.81632   0.99305     X

470           6   7.8940 0.045485 -1.89400 -2.27988 R

471           6   7.9181 0.046077 -1.91810 -2.30898 R

475           6   7.7735 0.042763 -1.77349 -2.13445 R

483           6   7.9181 0.046077 -1.91810 -2.30898 R

499          10   8.2796 0.056437   1.72037   2.07256 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

Response: Glucose           Model: carb_intake

Answer 1

Ans 1 ) the value of R 2 = 0.53 so r = 0.728 ,so there is 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 = 4.44742 + 0.0241019 Glucose

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

a.            Response: Hemoglobin Model: Glucoseb.           

General Regression Analysis: Hemoglobin versus Glucose

Regression Equation

Hemoglobin = 4.44742 + 0.0241019 Glucose

Coefficients

Term         Coef   SE Coef        T      P

Constant 4.44742 0.124943 35.5957 0.000

Glucose   0.02410 0.001017 23.6982 0.000

Summary of Model

S = 0.831988     R-Sq = 53.00%        R-Sq(adj) = 52.91%

PRESS = 348.310 R-Sq(pred) = 52.51%

Analysis of Variance

Source          DF   Seq SS   Adj SS   Adj MS        F          P

Regression       1 388.744 388.744 388.744 561.603 0.0000000

Glucose        1 388.744 388.744 388.744 561.603 0.0000000

Error          498 344.718 344.718    0.692

Lack-of-Fit 135 167.864 167.864    1.243    2.552 0.0000000

Pure Error   363 176.854 176.854    0.487

Total          499 733.462

Fits and Diagnostics for Unusual Observations

Obs Hemoglobin      Fit    SE Fit Residual St Resid

14          12 10.0150 0.121499   1.98503   2.41175 R X

17           6   7.7976 0.043273 -1.79759 -2.16352 R

22          12   9.6775 0.108033   2.32246   2.81529 R X

55          12   9.3883 0.096666   2.61168   3.16049 R X

74           6   7.7735 0.042763 -1.77349 -2.13445 R

84          11   9.5088 0.101378   1.49117   1.80576     X

88           6   7.8699 0.044908 -1.86990 -2.25078 R

99          11   8.3278 0.057982   2.67217   3.21961 R

133           6   7.7976 0.043273 -1.79759 -2.16352 R

138           6   7.8217 0.043801 -1.82169 -2.19261 R

142          10   8.1109 0.051299   1.88909   2.27490 R

152          10   7.9904 0.047940   2.00959   2.41943 R

159           6   7.8940 0.045485 -1.89400 -2.27988 R

161          11   8.5447 0.065267   2.45525   2.96019 R

165          6   7.8699 0.044908 -1.86990 -2.25078 R

173           6   7.7012 0.041344 -1.70118 -2.04725 R

189           6   7.8217 0.043801 -1.82169 -2.19261 R

192          10   9.7739 0.111861   0.22605   0.27419     X

202          10   8.0145 0.048588   1.98549   2.39052 R

218          10   8.1109 0.051299   1.88909   2.27490 R

223          12   9.7739 0.111861   2.22605   2.70010 R X

229           6   7.8458 0.044346 -1.84579 -2.22169 R

237          11   9.2196 0.090137   1.78040   2.15260 R

241          10   8.2073 0.054180   1.79268   2.15927 R

243          11   9.2196 0.090137   1.78040   2.15260 R

278          10   8.0627 0.049921   1.93729   2.33271 R

282           6   7.8458 0.044346 -1.84579 -2.22169 R

312           6   7.7012 0.041344 -1.70118 -2.04725 R

321          12 12.1600 0.209508 -0.16004 -0.19876     X

368          12   9.5811 0.104223   2.41887   2.93042 R X

375          11   8.9786 0.080983   2.02142   2.44121 R

385          11 10.1837 0.128295   0.81632   0.99305     X

470           6   7.8940 0.045485 -1.89400 -2.27988 R

471           6   7.9181 0.046077 -1.91810 -2.30898 R

475           6   7.7735 0.042763 -1.77349 -2.13445 R

483           6   7.9181 0.046077 -1.91810 -2.30898 R

499          10   8.2796 0.056437   1.72037   2.07256 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

Response: Glucose           Model: carb_intake