Question: Residual Analysis and Diagnostics

1. After running a regression model, y =  _ +  _{ } x _ +  _{  } x _ +  _{ } x _ +   , the model adequacy should be checked by performing a residual analysis. Check whether the following results justify the basic error term assumptions or not. When you look at the plots, can you see any unusual observations? State the assumptions that you are checking explicitly and use =0.05.
   
   Durbin-Watson statistic = 1.17113
2. Consider the regression model, y =  _ +  _{ } x _ +  _{  } x _ +  _{ } x _ +  _{ } x _ +   . By looking at the matrix plot below, what can you tell about the relationships between the predictors, i.e., do you think that there is multicollinearity between the independent variables? Support your answer by using the "VIF" values from the Minitab output.
   The regression equation is
   y1 = - 103 + 0.580 x1 + 0.839 x2 - 1.32 x3 + 0.160 x4
   Predictor Coef SE Coef T P VIF
   Constant -103.3 202.6 -0.51 0.618
   x1 0.5803 0.1087 5.34 0.000 1.011
   x2 0.8394 0.4607 1.82 0.088 19.755
   x3 -1.3168 0.2740 -4.81 0.000 1.001
   x4 0.1603 0.5529 0.29 0.776 19.801
   
3. A linear regression model, y =  _ +  _{ } x _ +  _{  } x _ +  , was fitted to 24 heat treatment data points, and the following Minitab spreadsheet records were produced. Which observations can be considered as outlier, leverage, or influential? State your reasons explicitly by referring to the diagnostics statistics.

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