Question

A total of 27,778,888 passengers passed through Frankfurt Airport in 2016, an increase of 11.3% from 2015. The Central Statistics Office wish to relate the number of passengers passing through the airport in a day (Y) to the total number of flights in and out of the airport on that day (X). A simple linear regression model is proposed for the data. The number of passengers and the combined number of flights on 100 randomly selected days are recorded. Summary statistics for these data are as follows:

Xx 2 i = 14, 499, 179, Xxiyi = 2, 174, 485, 000, x¯ = 379.23, y¯ = 56, 890 and MSE = 9, 428, 162.57.

a) The best fit (least squares) line is: ˆy = 1941.09 + 144.90x Interpret the estimate of the intercept and slope of the regression line in the context in which the data were collected.

b) Compute a 99% confidence interval for the slope of the regression line.

c) What are the assumptions underlying the simple linear regression model?

d) Briefly explain why it is important to check that the assumptions of the model have been satisfied?

Answer 1

Fitted model is given by

Intercept in the above fitted model gives us the expected mean of number of passengers passing through the airport in a day, y at x = 0

The slope of regression lines tells us that there would be 144.90 times difference in the predicted value of y for each unit difference in number of flights in and out of the airport on that day , x.

b) confidence interval for slope of line is given by

99% confidence interval for slope is given by

c) some of the assumptions simple linear regression model are:

i) The predictor y and explanatory variable x are linearly related.