STATISTICS 224        Assignment 11        Due  Apr. 30, 2004

Exercises from the textbook, "Probability & Statistics for Engineers"
by R. Johnson

Section 11.2:  11.2, 11.3 (for these, perform and show all basic calculations
needed), 11.10 (d) also provide 95% CI for beta_1; 11.11, 11.20 (c)-(d),
(e) also derive Var( b_1 ); 11.21 (but for observations in Exer. 11.10),
also, provide value of sample correlation r between x and Y

Section 11.5:  11.30, 11.31 (but for data in Exer. 11.30); 11.34,
11.35 (also, assess whether either or both of x_1 and x_2 are useful in
explaining behavior of Y)

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Output (partial) for Exercises 11.30 & 11.31:

> model2.lm <- lm(y ~ x + x^2)
> summary(model2.lm)

              Value Std. Error t value Pr(>|t|)
(Intercept)  1.7507  0.1942     9.0140  0.0000
          x -0.3163  0.0811    -3.8999  0.0059
        x^2  0.0253  0.0072     3.5210  0.0097

Residual standard error: 0.1651 on 7 degrees of freedom
Multiple R-Squared: 0.7055
F-statistic: 8.383 on 2 and 7 df, p-value is 0.01387

> anova(model2.lm)
Analysis of Variance Table
          Df Sum of Sq   Mean Sq  F Value      Pr(F)
        x  1 0.1191300 0.1191300
      x^2  1 0.3380485 0.3380485
Residuals  7 0.1908715 0.0272674
    Total  9 0.6480500


Output (partial) for Exercises 11.34 & 11.35:

> hardness.lm <- lm(y ~ x1 + x2)
> summary(hardness.lm)

                Value Std. Error   t value  Pr(>|t|)
(Intercept)  161.3365   11.4329    14.1117    0.0000
         x1   32.9687   16.7537     1.9678    0.0806
         x2   -0.0855    0.0098    -8.7351    0.0000

Residual standard error: 3.791 on 9 degrees of freedom
Multiple R-Squared: 0.8991
F-statistic: 40.09 on 2 and 9 df, p-value is 3.296e-05

> anova(hardness.lm)
Analysis of Variance Table

          Df Sum of Sq  Mean Sq  F Value      Pr(F)
       x1  1    55.651   55.651
       x2  1  1096.538 1096.538
Residuals  9   129.340   14.371
    Total 11  1281.529