Question

4. The following output was obtained as an analysis of variance table in R (two-way layout without replications), except that some of the values have been replaced by question marks. Analysis of Variance Table Response: y x1 x2 Residuals Signif. codes: (a) Give the equation to compute the sum of squares for $x_1$. Define all variables mentioned in your equation clearly. (b) Test the null hypothesis that the factor $x_2$ has no effect on the observations at level of significance $\alpha = 0.05$. (c) Test the null hypothesis that the means of all observations are equal at level of significance $\alpha = 0.05$. (d) Compute the maximum likelihood estimator for the common variance. Df Sum Sq Mean Sq F value Pr(>F) 2 3629.2 1814.58 12.8264 0.006811 3 1116.9 ????? ????? ????? ????? 6 ????? 141.47 0 '*' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 [5 marks] [6 marks] [8 marks] [6 marks]

          4. The following output was obtained as an analysis of variance table in R (two-way
layout without replications), except that some of the values have been replaced
by question marks.
Analysis of Variance Table
Response: y
x1
x2
Residuals
Signif. codes:
(a) Give the equation to compute the sum of squares for $x_1$. Define all
variables mentioned in your equation clearly.
(b) Test the null hypothesis that the factor $x_2$ has no effect on the observations
at level of significance $\alpha = 0.05$.
(c) Test the null hypothesis that the means of all observations are equal at level
of significance $\alpha = 0.05$.
(d) Compute the maximum likelihood estimator for the common variance.
Df Sum Sq Mean Sq F value Pr(>F)
2 3629.2 1814.58 12.8264 0.006811 **
3 1116.9 ????? ????? ????? ?????
6 ????? 141.47
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[5 marks]
[6 marks]
[8 marks]
[6 marks]

4. The following output was obtained as an analysis of variance table in R (two-way
layout without replications), except that some of the values have been replaced
by question marks.
Analysis of Variance Table
Response: y
x1
x2
Residuals
Signif. codes:
(a) Give the equation to compute the sum of squares for x1. Define all
variables mentioned in your equation clearly.
(b) Test the null hypothesis that the factor x2 has no effect on the observations
at level of significance α = 0.05.
(c) Test the null hypothesis that the means of all observations are equal at level
of significance α = 0.05.
(d) Compute the maximum likelihood estimator for the common variance.
Df Sum Sq Mean Sq F value Pr(>F)
2 3629.2 1814.58 12.8264 0.006811 **
3 1116.9 ????? ????? ????? ?????
6 ????? 141.47
0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
[5 marks]
[6 marks]
[8 marks]
[6 marks]

Added by Edward C.

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