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In 1969, all field goal attempts in the National Football League and American Football League were analyzed. See Table A.15. (The data has been summarized: all attempts between 10 and 19 yards from the goal post are listed as 14.5 yards out, etc.)

Successful fraction of field goal attemptsDistance from goal, x yards14.524.534.544.552.05058Fraction successful, Y0.900.750.540.\begin{matrix} \text{Successful fraction of field goal attempts}\\ \text{Distance from goal, x yards} & \text{14.5} & \text{24.5} & \text{34.5} & \text{44.5} & \text{52.0} & \text{50} & \text{58}\\ \text{Fraction successful, Y} & \text{0.90} & \text{0.75} & \text{0.54} & \text{0.29} & \text{0.15} & \text{6.1} & \text{6.7}\\ \end{matrix}

Find the exponential regression function; graph it with the data. What success rate does this function predict from a distance of 50 yards?


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