STATISTICS 324        Assignment 12        Due  Apr. 30, 2004

Exercises from the textbook, "Probability & Statistics for Engineering"
by J. Devore

Section 12.1:  4, 9;  Section 12.2:  12 (perform and show all basic
calculations needed), 17, 20 (e. also obtain a scatter plot of the data,
comment on any `special/unusual' features, e.g., any outlying values?)

Section 12.3:  31 (but using data from Exer. 12; c. also, determine value of the
sample correlation r between x and Y), 34 (a. that is, test  H_0 : beta_1 = 0
versus  H_a : beta_1 != 0; also verify that [t_{b_1}]^2 = F, the F-statistic
from ANOVA results)

Section 12.4:  44 (a)-(c), 46 (e. also calculate 90% prediction interval for
silver of a crystal when x = 500)

Section 13.3:  30;   Section 13.4:  44
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R-output (partial) for Exercise 20, Sec. 12.2

> lichen.lm <- lm(y ~ x)
> summary(lichen.lm)

             Value Std. Error t value Pr(>|t|)
(Intercept) 0.3651 0.0990     3.6863  0.0036
          x 0.9668 0.1829     5.2856  0.0003

Residual standard error: 0.1932 on 11 degrees of freedom
Multiple R-Squared: 0.7175
F-statistic: 27.94 on 1 and 11 df, p-value is 0.0002581

> anova(lichen.lm)
Analysis of Variance Table

          Df Sum of Sq  Mean Sq F Value        Pr(F)
        x  1  1.042750 1.042750 27.9372 0.0002580675
Residuals 11  0.410573 0.037325
    Total 12  1.453323


R-output (partial) for Exercise 44, Sec. 13.4

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

              Value Std. Error t value Pr(>|t|)
(Intercept) 19.4398  2.1883     8.8835  0.0000
         x1  1.4423  0.2076     6.9462  0.0000
         x2  0.3356  0.0181    18.5067  0.0000

Residual standard error: 1.094 on 25 degrees of freedom
Multiple R-Squared: 0.9645
F-statistic: 339.3 on 2 and 25 df, p-value is 0

> anova(wheat.lm)
Analysis of Variance Table

          Df Sum of Sq  Mean Sq  F Value        Pr(F)
       x1  1  402.3732 402.3732
       x2  1  410.0064 410.0064
Residuals 25   29.9276   1.1971
    Total 27  842.3071