Question

In a study on the estimation of attendance at the Fortifications of Quebec National Historic Site, we want to assess the reliability of magnetic counters used to measure the variation in temporal attendance. Three days of investigation were chosen to represent each day of the week and the evaluation took place over 23 days, and this in two schedules to cover attendance not only during the day, but also early in the evening. The number of people attending the Fortifications was counted manually. We have also noted the number of passages perceived by the magnetic counters. We want to perform a simple linear regression between the actual number of people enumerated manually and the number of passes perceived by the magnetic counters. A) We want to analyze the regression model passing through the origin. i) What is the empirical regression equation? ii) What is the standard error associated with the regression coefficient? iii) Is the regression equation passing through the origin significant, at the threshold 5%? B) Determine a 95% confidence interval for the actual average number of people through out a day at the Fortifications-de-Québec, if the number of passages perceived by the magnetic counter is 52.

Answer 1

o The empirical reprenim equation r the given -2.39 data 2.3167 X + + e o - standard m st error of 18 9.186 estimate for a regression o = longinn of coefficient Aloo standard error SELBD = 2.942 SECB) = 0.010 T (111) yeh regremion origine, cut the line is thershold parring - 5% through . (0) 95 %. contidence interway for actual awareege number of people out a day at the fortification Qubec, if number of pasreger Precived by magnetic counter the through de in 52 Yux & tca/2, n. y 14 (X07) VD Yux = -2.391 + 2.3167852 - 118. 078 Sxx Exi2_nx2 = 39268 - 48x 25. 739 Sxy = 38084

Hext tease, nar) . It cxo-x? nosxx tot past 118.072 0153 x 9.44 lsa (52-25.73) * Jur 38084 1 H8 87 13.7982 brobople ( 114.212 121.87 S ople Bolio blabor