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[M] A healthy child's systolic blood pressure $p$ (in millimeters of mercury) and weight $w$ (in pounds) are approximately related by the equation$\beta_{0}+\beta_{1} \ln w=p$Use the following experimental data to estimate the systolic blood pressure of a healthy child weighing 100 pounds.

$\hat{\beta}=\left[\begin{array}{l}{18.56} \\ {19.24}\end{array}\right]$$v(4.5)=53.0 \mathrm{ft} / \mathrm{s}$

Calculus 3

Chapter 6

Orthogonality and Least Square

Section 6

Applications to Linear Models

Vectors

Oregon State University

Harvey Mudd College

Idaho State University

Boston College

Lectures

02:56

In mathematics, a vector (…

06:36

02:40

(a) Convert normal blood p…

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02:26

00:07

The following chart define…

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The normal systolic blood …

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A formula for the normal s…

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we're essentially trying to sew to solve our least squares problem. So I've already returned a Matic sacks and being containing the data that were given and because you want to form the normal equations I've already computed the mattress is X transpose X and X transpose speak. There's just a simple computation you can check yourself now we we know that the vector containing the confusions that we've want beat the hat satisfies the normal equation. X transpose X meat on is equal to X transpose. Why? So I made a hat. He's obtained by computing X transpose x inverse that multiplies X transpose y now excellent was actually two by two matrix. So it's me howto find the timbers so one over its determinant the medics obtain by swapping your mints on the main diagonal and negating the elements and secondary diagonal that multiplies X transpose. Why that we've completed already? I've done these multiplication for you and the result is 18.56 19.23. Therefore, we know that the linear model they were looking for, he's but I sure is estimated by 18.56 which is the constant term plus the leaner term, which is 19.23. And of course the problem was restated in term of longer than off the weights. So this formula is to wait the pressure in term, off the weight. Now, if the way is ah 100 then we can estimate the pressure to be roughly 18.56 plus 19.23. The longer rhythm off 100. And you can do these with a calculator. The result is other and 7.12.

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