Use SPSS to answer the questions below. Interpret the output: running the test alone will not give you full credit.   Keep in mind the requirements spelled out at the beginning of this assignment as well for any hypothesis testing questions.

1. The table below provides information on a dependent variable y, and independent variables x1, x2, x3, x4 and x5. Using SPSS output, answer the questions given below the table.

y x1     x2    x3      x4        x5

110   5       83  1.7       34 1.3

132   7      77  2.14     24 1.6

156 11   74   3.16    22 2.6

  89   4   96   1.78    54 1.1

126 10   56   3.54    43 2.7

121 12   64   3.13    20 1.9

114   6   82   2.67    39 2.5

104   5   98   2.94    38 2.7

  98   3 102   1.99    41 2.4

  84   1 104   1.68    49 1.7

112   7   84   1.96    32 1.9

  94   4   99   2.18    56 2.3

  92   3   94   2.16    67 2.5

  85   2   86   1.96    45 2.9

108   6   78   2.96    32 2.7

127 11   79   3.12    27 2.9

128   9   56     3.1    24 2.8

  78   4 112   1.75    43 3.1

  89   5   98   1.67    42 2.5

  95   3   95   1.99    21 2.3

a. Use a matrix plot to determine whether the variables are linearly related. Interpret your result.

b. Plot a histogram and a normal probability plot for standardized residuals.

c. Are the assumptions for regression met?

d. Find the regression equation. 

e. What is the standard error of the estimate? Interpret its value. 

f. What is the coefficient of determination? What does this value tell you? 

g. What is the coefficient of determination adjusted to degrees of freedom? Why does this value differ from the coefficient of determination? 

h. Test the validity of the model. What does the p-value of the test statistic tell you? 

i. Interpret each of the coefficients. 

j. Test to determine whether each of the independent variables is linearly related to the dependent variable. 

k. Run a step-wise regression and comment on the new model.

l. Are any of the variables excluded in the new model? If so, name them.