HP HP-15C - Polar and Rectangular Coordinate Conversions

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Section

Using Matrix Operations

1 31

Keystrokes

Display

-9.2337

5.3446

-2.2599

5.3494

-2.4212

5.3494

-05

-06

-05

The

output voltage

5.3494

-2.4212C

Displays

74|.

Calculates

=(R3)\I4\.

Deactivates User mode.

Least-Squares

Using

Normal

Equations

The

unconstrained least-squares problem

known

statistical

literature

multiple linear regression.

uses

the

linear model

Here,

61;

...,

are the

unknown parameters,

x^,

...,

are the

independent

(or

explanatory) variables,

y is the

dependent

(or

response)

variable,

and r is the

random error having expected

value

E(r)

= 0,

variance

a2.

After

making

observations

of y and

x1(

x%,

...,

xp,

this

problem

can

expressed

+ r

where

y is an n

-vector,

X is an n X p

matrix,

and r is an

-vector

consisting

of the

unknown random errors satisfying

E(r)

= 0 and

the

model

correct

and

has an

inverse, then

the

calculated

least-squares solution

b =

(XrX)"1X-ry

has the

following

properties:

•

E(b)

b, so

that

is an

unbiased estimator

Cov(b)

E((b

b)T(b

b))

a2(XrX)"1,

the

covariance matrix

the

estimator

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