Perform canonical correlation analysis for a sample data set.

The data set `carbig`

contains measurements for 406 cars from the years 1970 to 1982.

Load the sample data.

Define X as the matrix of displacement, horsepower, and weight observations, and `Y`

as the matrix of acceleration and MPG observations. Omit rows with insufficient data.

Compute the sample canonical correlation.

View the output of `A`

to determine the linear combinations of displacement, horsepower, and weight that make up the canonical variables of `X`

.

A = *3×2*
0.0025 0.0048
0.0202 0.0409
-0.0000 -0.0027

`A(3,1)`

is displayed as `—0.000`

because it is very small. Display `A(3,1)`

separately.

The first canonical variable of `X`

is `u1 = 0.0025*Disp + 0.0202*HP — 0.000025*Wgt`

.

The second canonical variable of `X`

is `u2 = 0.0048*Disp + 0.0409*HP — 0.0027*Wgt`

.

View the output of B to determine the linear combinations of acceleration and MPG that make up the canonical variables of `Y`

.

B = *2×2*
-0.1666 -0.3637
-0.0916 0.1078

The first canonical variable of `Y`

is `v1 = `

`—`

`0.1666*Accel — 0.0916*MPG`

.

The second canonical variable of `Y`

is `v2 = —0.3637*Accel + 0.1078*MPG`

.

Plot the scores of the canonical variables of `X`

and `Y`

against each other.

The pairs of canonical variables $$\{{u}_{i},{v}_{i}\}$$ are ordered from the strongest to weakest correlation, with all other pairs independent.

Return the correlation coefficient of the variables `u1`

and `v1`

.