Question

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Answer 1

The r.m.s. error of the regression line is found from
\[\sqrt{(1-r ^{2})}\times S.D.\ of\ y=\sqrt{1-(0.55)^{2}}\times 0.5=0.4176\ inch\]
Since the scatter diagram is football-shaped, the r.m.s. error of the regression line can be used like standard deviation for the regression line.
\[z=\frac{0.5}{0.4176}\approx 1.2\]
By reference to a standard normal distributon table, the regression line is found to overestimate head circumference in about 11.5% of cases.