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4 years ago

Please help me with these. Thanks

Mathematics

1 answer:

DIA [1.3K]4 years ago

6 0

5.

f(K) = D^3 => f(25) = 125 => 25 * t = 125 ( because K is directly proportional with D^3 )=> t = 125 / 25 => t = 5 => f(25) = 25 * 5 => K * 5 = D^3 ;

6.

f(L) = F^3 => f(2) =3^3 =>f(2) = 27 => 2 / t =27 => t = 2 / 27 => t = 0.074 => f(2) = 2 / 0.074 => K / 0.074 = F^3 ;

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a) $y=-0.317 x +46.02$

b) Figure attached

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Step-by-step explanation:

We assume that th data is this one:

x: 30, 30, 30, 50, 50, 50, 70,70, 70,90,90,90

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$m=\frac{S_{xy}}{S_{xx}}$

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$\sum_{i=1}^n x^2_i =30^2+30^2+30^2+50^2+50^2+50^2+70^2+70^2+70^2+90^2+90^2+90^2=49200$

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With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=49200-\frac{720^2}{12}=6000$

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And we can find the intercept using this:

$b=\bar y -m \bar x=27-(-0.317*60)=46.02$

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In oder to calculate S^2 we need to calculate the MSE, or the mean square error. And is given by this formula:

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The degred of freedom for the error are given by:

$df_{E}=n-2=12-2=10$

We can calculate:

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And now we can calculate the sum of squares for the regression given by:

$SSR=\frac{S^2_{xy}}{S_{xx}}=\frac{(-1900)^2}{6000}=601.67$

We have that SST= SSR+SSE, and then SSE=SST-SSR= 792-601.67=190.33[/tex]

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$S^2=\hat \sigma^2=MSE=\frac{190.33}{10}=19.03$

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