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The correlation is defined as r=cov(x,y)/sd(x)/sd(y). We also know that for linear regression r^2=R^2. In addition, the slope, m=cov(x,y)/var(x).
Using all the above we get that R^2=m^2var^2(x)/sd^2(x)sd^2(y). Or that 0.4=m^2*4^4/4^2/8^2 and that m=1.26
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Day 6: Correlation and Regression Lines #2
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The correlation is defined as r=cov(x,y)/sd(x)/sd(y). We also know that for linear regression r^2=R^2. In addition, the slope, m=cov(x,y)/var(x).
Using all the above we get that R^2=m^2var^2(x)/sd^2(x)sd^2(y). Or that 0.4=m^2*4^4/4^2/8^2 and that m=1.26