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        Psychology 406

        Assignment \#8


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Consider the following set of numbers representing matched
observations on two variables:

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\begin{tabular}{cc}

Variable 1 & Variable 2 \\

  95  & 31   \\

   100     &  31   \\

    100        &  31  \\

        102        &  32   \\

         103           & 32   \\

           105             &  32   \\

          106                  &  33   \\

           106                     & 33   \\

            106                        & 33    \\

                109                        & 34   \\

                110                            & 34   \\


                                          110      & 34   \\

      111   &  35  \\

      112       & 35   \\

      112           & 35    \\

       114              & 36   \\

          114               & 36   \\

            115                 & 36   \\

                    117             & 37   \\

                     118                & 37   \\

130 & 37 \\

\end{tabular}

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\begin{tabular}{ccc}

Variable 1 & & Variable 2 \\

Sum: 2,295 & & Sum: 714 \\

Sum Squares: 251,991 & & Sum Squares: 24,360 \\

 & Sum of Cross Products: 78,323 & \\

 \end{tabular}

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 i) Construct a scatterplot for these two variables (placing
 variable 2 along the abscissa --- i.e., along the ``x axis'').

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 ii) Find the least-squares line for predicting variable 1 from
 variable 2 and plot it on the scatterplot constructed in (i).

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 iii) Calculate the correlation between the two variables and give
 the percentage of sample variance for variable 1 that is
 ``accounted for'' by variable 2 in terms of a linear relationship.

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 iv) Obtain the usual sample variance of estimate and its unbiased
 counterpart.






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