A firm called "BetaFix" developed proprietary software that corrects beta

estimates. The only known information about their top$-$secret algorithm is that

the transformation of betas that it carries out is linear.

You ask for a demonstration from a sales representative of "BetaFix" and

provide two values of uncorrected betas: $1\mathrm{.}7$ and $0\mathrm{.}4.$ The "BetaFix Ver. $2\mathrm{.}1"$

$($the most recent version of the proprietary software that corrects beta$)$ goes to

work and, after $16$ minutes of calculations, provides the two corrected betas:

$1\mathrm{.}11$ and $0\mathrm{.}72,$ respectively.

You think for a split second and declare your unwillingness to pay even a single

dime for this appliance because you know exactly how it works. The "BetaFix"

sales representative stares at you in disbelief, challenging you to provide the

corrected value of beta if the uncorrected beta is $1\mathrm{.}1.$

You smile, write down the correct answer on a piece of paper, and pass it to the

sales representative. What was the correct answer you have written on the

piece of paper?