1. Your colleague decides to develop a regression model to predict Quality
   from Size. She computes the following statistics for the data collected:

      Size (LOC): Mean=1200; Standard deviation=32
      Quality: Mean=40; Standard deviation=10
      Correlation between Quality and Size is -0.8

    a) Given these statistics and the correlation coefficient above derive and 
       state the regression equation for these data.

            Since we wish to predict Quality then Quality is on the 
            y-axis. Hence b=r(s(y)/s(x))=-0.8(10/32)=-0.25 and
            a=ybar-b(xbar)=40-(-0.25)(1200)=340

                        Quality = 340 - 0.25(Size)
            
 
    b) From your answer to question 2. a), answer the following:

       i) Predict the quality of a program of size 200.
 
                        Quality = 340 - 0.25(200) = 290
                     
 
      ii) Interpret the coefficients of the regression equation.
         
            SLOPE: For unit increase in size, quality may be expected
                   to decrease by 0.25 units.
            INTERCEPT: For size of zero quality would be expected to be
                   340 units. Since a module of size zero is not a module
                   this does not make sense.



2. Your colleague decides to develop a regression model to predict Reliability 
   from Size. She computes the following statistics for the data collected:

      Size (LOC): Mean=400; Standard deviation=24
      Reliability: Mean=50Hrs; Standard deviation=20Hrs
      Correlation between Reliabilty and Size is -0.6

    a) Given these statistics and the correlation coefficient above derive and 
       state the regression equation for these data.

            Since we wish to predict Reliability then Reliability is
            on the y-axis. Hence b=r(s(y)/s(x))=-0.6(20/24)=-0.5 and
            a=ybar-b(xbar)=50-(-0.5)(400)=250

                        Reliability = 250 - 0.5(Size)
            
 
    b) From your answer to question 2. a), answer the following:

       i) Predict the reliability of a program of size 300.
 
                        Reliability = 250 - 0.5(300) = 100
                     
 
      ii) Interpret the coefficients of the regression equation.
         
            SLOPE: For unit increase in size, reliability may be expected
                   to decrease by 0.5 hours.
            INTERCEPT: For size of zero reliability would be expected to be
                   250 hours. Since a module of size zero is not a module
                   this does not make sense.