Question

Suppose that we want to find a regression equation relating systolic blood pressure (y) to weight (x1), age (x2) and smoking status (0  =  does not smoke, 1  =  smokes less than one pack per day, 2  =  smokes one or more packs per day). Use the Minitab outputs below to test whether or not the smoking status variable adds to the predictive value of a model which already contains weight and age, using α  =  .05. i.e., test the hypothesis H0 : β4  =  β5  =  0 vs H1 :  at least one of β4, β5  ≠  0 in the model  y  =  β0 + β1x1 + β2x2 + β3x3 + β4x4 + β5x5. ------------------------------------------ Regression Analysis: SYSTOLIC versus WEIGHT, AGE Source DF Adj SS Adj MS F-Value P-Value Regression 2 9890.9 4945.45 59.88 0.000 WEIGHT 1 1618.8 1618.81 27.33 0.000 AGE 1 4108.4 4108.44 69.36 0.000 Error ? 6193.9 82.59 Lack-of-Fit ? 4529.4 59.76 7.47 0.285 Pure Error 1 1664.5 8.00 Total ? 16084.8 S R-sq R-sq(adj) R-sq(pred) 9.088 61.49 % 63.54% 61.70% Term Coef SE Coef T-Value P-Value VIF Constant 87.90 3.97 22.11 0.000 WEIGHT 0.1529 0.0293 5.23 0.000 1.27 AGE 0.5053 0.0607 8.33 0.000 1.27 ------------------------------------------ Regression Analysis: SYSTOLIC versus WEIGHT, AGE, x4, x5 Source DF Adj SS Adj MS F-Value P-Value Regression 4 10372.4 2593.10 33.14 0.000 WEIGHT 1 1572.9 1572.93 26.16 0.000 AGE 1 4133.6 4133.55 68.74 0.000 x4 1 6.7 6.69 0.11 0.739 x5 1 29.3 29.34 0.49 0.487 Error ? 5712.3 78.25 Lack-of-Fit ? 5704.3 79.23 7.59 0.283 Pure Error 1 8.0 8.00 Total ? 16084.8 Term Coef SE Coef T-Value P-Value VIF Constant 86.91 4.52 19.23 0.000 WEIGHT 0.1518 0.0297 5.11 0.000 1.29 AGE 0.5105 0.0616 8.29 0.000 1.29 x4 0.75 2.25 0.33 0.739 2.10 x5 1.63 2.33 0.70 0.487 2.11 ------------------------------------------ What is the value of the test statistic? (2 decimals)

Answer 1

sample size n=			78
SSE for complete model :SSEc =			5712.3
SSE for reduced model :SSER =			6193.9
c =coefficients in complete model =			4
r =coefficient in reduced model =			2
Partial F=((SSEr-SSEc)/(c-r))/(SSEc/(n-c-1)) =					3.08