Question 25
A group of students is preparing for semester exams. A teacher wants to predict scores from daily study hours. The data for four students appears in the source tables. The proposed English model is $y=2x+b$, where $b\in\mathbb R,b>0$. The printed quadratic loss function is reproduced below; each displayed residual reads $y_i-y_i$. It is described as measuring the difference between predicted and actual values. Algorithm 1 approximates a minimum by sweeping from $a=0$ to $c=10$ in increments $\Delta=0.1$. Initialize $\mathrm{min\_t}=a$, $\mathrm{min\_L}=L(a)$, $t=a$; while $t\le c$, compute $\mathrm{value}=L(t)$, replace the stored minimum and minimizer if $\mathrm{value}<\mathrm{min\_L}$, then set $t=t+\Delta$. Output $(\mathrm{min\_t},\mathrm{min\_L})$. All original tables, formulas and both algorithm panels are retained below.
Using Algorithm 1, calculating $L(t)$ at the 9th step gives A. Using the model and mathematical tools, the minimum of $L(b)$ is B (A is called an approximation to B). Find $A-B$, with all results rounded to hundredths.
Using Algorithm 1, calculating $L(t)$ at the 9th step gives A. Using the model and mathematical tools, the minimum of $L(b)$ is B (A is called an approximation to B). Find $A-B$, with all results rounded to hundredths.