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Homework Statement
Let [itex]x_{1},...,x_{n}[/itex] be n observations. If [itex]y_{1},...,y_{n}[/itex] is another set of observations s.t. [itex]y_{i}=ax_{i}+b[/itex] , prove that [itex]s_{y}=|a|s_{x}[/itex] .
The Attempt at a Solution
Attempt at a proof: Since [itex]\bar{y}=a\bar{x} +b[/itex] then [itex]\bar{x}=(\bar{y}-b)/a[/itex] and [itex]s_{x}=\sqrt{\frac{1}{n-1}\sum(x_{i}-\frac{\bar{y}-b}{a})}[/itex]. This is where I get stuck. Any ideas?