The Complete Second-Order Model Was Fit To $n = 25$ Data Points

question 116

Essay

The complete second-order model $E ( y ) = \beta _ { 0 } + \beta _ { 1 } x _ { 1 } + \beta _ { 2 } x _ { 2 } + \beta _ { 3 } x _ { 1 } x _ { 2 } + \beta _ { 4 } x _ { 1 } ^ { 2 } + \beta _ { 5 } x _ { 2 } ^ { 2 }$ was fit to $n = 25$ data points. The printout is shown below.
ANOVA
$\begin{array} { l l l l l l } & d f & \text { SS } & \text { MS } & F & \text { Significance } F \\\hline \text { Regression } & 5 & 22812.46538 & 4562.493077 & 56487.98 & 6.12671 \mathrm { E } - 39 \\\text { Residual } & 19 & 1.534616187 & 0.080769273 & & \\\text { Total } & 24 & 22814 & & & \\\hline\end{array}$

$\begin{array}{lllllll} & \text { Coefficients } & \text { Standard Error } & t \text { Stat } & \text { P-value } & \text { Lower 95\% } & \text { Upper 95\% } \\\hline \text { Intercept } & -0.202274307 & 0.377603882 & -0.535678569 & 0.598396064 & -0.99260856 & 0.588059946 \\\mathrm{X} 1 & 0.57956491 & 0.184697537 & 3.137913578 & 0.005416889 & 0.192988402 & 0.966141418 \\\mathrm{X} 2 & 0.502983937 & 0.130940123 & 3.841327815 & 0.001100855 & 0.228923024 & 0.777044849 \\\mathrm{Xl}^{*} \mathrm{X} 2 & 1.976110807 & 0.022011043 & 89.77815357 & 1.92982 \mathrm{E}-26 & 1.93004115 & 2.022180464 \\\mathrm{X} 1^{\wedge} 2 & -0.026825292 & 0.025350994 & -1.058155454 & 0.303252905 & -0.079885548 & 0.026234964 \\\mathrm{X}^{\wedge} 2 & 0.012944358 & 0.015088978 & 0.857868446 & 0.401657492 & -0.018637245 & 0.044525961\end{array}$

a. Write the complete second-order model for the data.
b. Is there sufficient evidence to indicate that at least one of the parameters $\beta _ { 1 } , \beta _ { 2 } , \beta _ { 3 } , \beta _ { 4 }$ , and $\beta 5$ is nonzero? Test using $\alpha = .05$ .
c. Test $H _ { 0 } : \beta _ { 3 } = 0$ against $H _ { \mathrm { a } } : \beta _ { 3 } \neq 0$ . Use $\alpha = .01$ .
d. Test $H _ { 0 } : \beta _ { 4 } = 0$ against $H _ { \mathrm { a } } : \beta _ { 4 } \neq 0$ . Use $\alpha = .01$ .

Identify the differences and similarities in cell division among different organisms and cell types.

Understand the concept of virtualization in computing and its purposes.

Identify the characteristics and structures of different network topologies.

Recognize security measures implemented in networked environments.

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