Explanation Given: The average delay in minutes for departures and arrivals of domestic flights at O’Hare Airport in Chicago for selected years is as shown below. Average delay in departures ( x ) Average delay in arrivals ( y ) 63.7 72.4 57.9 64.4 56.7 64.4 59.4 68.5 58.4 67.4 60.7 70.8 Concept used: Given ordered pairs ( x , y ) with sample means x ¯ and y ¯ , sample standard deviations s x and s y and the correlation coefficient γ , the equation of the least squares regression line for predicting y from x is, y ^ = b 0 + b 1 x , where b 1 = γ s y s x is the slpoe and b 0 = y ¯ − b 1 x ¯ is the y − intercept . First we find the sample means x ¯ and y ¯ . x ¯ = ∑ x n = 356.8 6 = 59.466666 y ¯ = ∑ y n = 407.9 6 = 67.983333 Now to find standard deviations, we construct the table as shown below: x y ( x − x ¯ ) 2 ( y − y ¯ ) 2 63.7 72.4 17.921116 19.506947 57.9 64.4 2.454442 12.840275 56.7 64.4 7.654440 12.840275 59.4 68.5 0.004444 0.2669447 58.4 67.4 1.137776 0.340277 60.7 70.8 1.521112 7.933612 ∑ ( x − x ¯ ) 2 = 30.69333 ∑ ( y − y ¯ ) 2 = 53.7283307 Therefore, standard deviations are, s x = ∑ ( x − x ¯ ) 2 n − 1 = 30.69333 6 − 1 = 30.69333 5 = 6.138666 = 2.4776 s y = ∑ ( y − y ¯ ) 2 n − 1 = 53

1st Edition

ISBN: 9781260722031

Author: Navidi

Publisher: McGraw-Hill Publishing Co.

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To find the least square regression line for the given data

Solution Summary: The author explains that the least square regression line is y=6.195+1.2474x, given the average delay in minutes for departures and arrivals of domestic flights at O’Hare Airport in Chicago.

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