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: Glucose           Model: carb_intake

   General Regression Analysis: Glucose versus Carb_Intake

   Regression Equation

   Glucose = 60.6392 + 0.266471 Carb_Intake

   Coefficients

   Term            Coef SE Coef        T      P

   Constant     60.6392 4.50657 13.4557 0.000

   Carb_Intake   0.2665 0.02014 13.2321 0.000

   Summary of Model

   S = 31.5315     R-Sq = 26.01%        R-Sq(adj) = 25.86%

   PRESS = 498939 R-Sq(pred) = 25.44%

   Analysis of Variance

   Source          DF Seq SS Adj SS Adj MS        F          P

   Regression       1 174079 174079 174079 175.088 0.0000000

   Carb_Intake    1 174079 174079 174079 175.088 0.0000000

   Error          498 495129 495129     994

   Lack-of-Fit 223 259995 259995    1166    1.364 0.0072711

   Pure Error   275 235135 235135     855

   Total          499 669208

   Fits and Diagnostics for Unusual Observations

   Obs Glucose      Fit   SE Fit Residual St Resid

   14      231 171.225 4.31408    59.775   1.91373     X

   22      217 153.638 3.08867    63.362   2.01921 R

   24      171 106.472 1.62945    64.528   2.04919 R

   61      154   90.217 2.48398    63.783   2.02913 R

   65      175 181.351 5.04351    -6.351 -0.20403     X

   81      122 160.033 3.52559   -38.033 -1.21380     X

   84      210 104.607 1.70446   105.393   3.34736 R

   98      122 159.233 3.47030   -37.233 -1.18805     X

   105      169   98.745 1.98743    70.255   2.23254 R

   113      175 107.538 1.59062    67.462   2.14224 R

   138      140 163.497 3.76699   -23.497 -0.75057     X

   192      221 100.077 1.91780   120.923   3.84211 R

   213      119 161.099 3.59957   -42.099 -1.34392     X

   223      221 138.982 2.16317    82.018   2.60730 R

   233       75 139.248 2.17849   -64.248 -2.04247 R

   237      198 113.400 1.44023    84.600   2.68582 R

   256      186 103.275 1.76299    82.725   2.62769 R

   270      162   93.682 2.27332    68.318   2.17232 R

   285      188 175.222 4.60062    12.778   0.40964     X

   301      176 160.299 3.54406    15.701   0.50111     X

   321      320 130.988 1.74993   189.012   6.00365 R

   334      181 162.964 3.72968    18.036   0.57604     X

   385      238 125.925 1.55424   112.075   3.55872 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 Glucose

   Residual Histogram for Glucose

Answer 1

Ans 1 ) the value of R 2 =0.2601so r =0.51 ,so there is not strong but moderate 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

Glucose = 60.6392 + 0.266471 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: Glucose           Model: carb_intake

General Regression Analysis: Glucose versus Carb_Intake

Regression Equation

Glucose = 60.6392 + 0.266471 Carb_Intake

Coefficients

Term            Coef SE Coef        T      P

Constant     60.6392 4.50657 13.4557 0.000

Carb_Intake   0.2665 0.02014 13.2321 0.000

Summary of Model

S = 31.5315     R-Sq = 26.01%        R-Sq(adj) = 25.86%

PRESS = 498939 R-Sq(pred) = 25.44%

Analysis of Variance

Source          DF Seq SS Adj SS Adj MS        F          P

Regression       1 174079 174079 174079 175.088 0.0000000

Carb_Intake    1 174079 174079 174079 175.088 0.0000000

Error          498 495129 495129     994

Lack-of-Fit 223 259995 259995    1166    1.364 0.0072711

Pure Error   275 235135 235135     855

Total          499 669208

Fits and Diagnostics for Unusual Observations

Obs Glucose      Fit   SE Fit Residual St Resid

14      231 171.225 4.31408    59.775   1.91373     X

22      217 153.638 3.08867    63.362   2.01921 R

24      171 106.472 1.62945    64.528   2.04919 R

61      154   90.217 2.48398    63.783   2.02913 R

65      175 181.351 5.04351    -6.351 -0.20403     X

81      122 160.033 3.52559   -38.033 -1.21380     X

84      210 104.607 1.70446   105.393   3.34736 R

98      122 159.233 3.47030   -37.233 -1.18805     X

105      169   98.745 1.98743    70.255   2.23254 R

113      175 107.538 1.59062    67.462   2.14224 R

138      140 163.497 3.76699   -23.497 -0.75057     X

192      221 100.077 1.91780   120.923   3.84211 R

213      119 161.099 3.59957   -42.099 -1.34392     X

223      221 138.982 2.16317    82.018   2.60730 R

233       75 139.248 2.17849   -64.248 -2.04247 R

237      198 113.400 1.44023    84.600   2.68582 R

256      186 103.275 1.76299    82.725   2.62769 R

270      162   93.682 2.27332    68.318   2.17232 R

285      188 175.222 4.60062    12.778   0.40964     X

301      176 160.299 3.54406    15.701   0.50111     X

321      320 130.988 1.74993   189.012   6.00365 R

334      181 162.964 3.72968    18.036   0.57604     X

385      238 125.925 1.55424   112.075   3.55872 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 Glucose

Residual Histogram for Glucose