Assignment 2

1. An airline was interested in comparing the estimated time of arrival (ETA) and the actual time of arrival (ATA) for domestic flights. To do this a random sample of 20 flights was taken over the past month for flights with ETAs in the time frame from noon until 7:00pm. These data are shown here in order of ETA.

Note please, that for notation reasons the time is recorded with decimal values as follows (e.g. 6.45 reads \(6: 45 \mathrm{pm})\)

Parts (c) to (h) are to be done by hand and then the results verified by SAS in part (i)

1. Plot a scatter diagram (using SAS, see part (i)) to get an idea of the form of the relationship between the ETA and the ATA. Does the scatter diagram indicate an approximately straight line?
2. State a SLR model making sure you give all assumptions necessary for statistical inference.
3. Find the least squares estimates of \(\beta_{0}\) and \(\beta_{1}\). Find the least squares fitted regression line.
   For the rest of the question assume that the assumptions hold.
4. Find \(s^{2}\), an estimate of \(\sigma^{2}\).
5. Use the t-test to test whether there is a significant linear relationship between the ATA and ETA. Use \(\alpha=0.05\).
6. Find a 95\% confidence interval for \(\beta_{1}\).
7. Set up the ANOVA table and hence test whether there is a significant linear relationship between the ATA and ETA. Use \(\alpha=0.05 .\)
8. Find the values of the coefficient of correlation, \(r\), and coefficient of determination, \(r^{2}\), and interpret their meanings in this problem.
9. Verify your above results using software

2. Refers to question 1 .

1. Find a 95% Confidence Interval for the mean value of the response variable (i.e. of the Actual arrival time) and a 95% Prediction Interval for an individual value of this response variable when the estimated arrival time is \(6: 50 \mathrm{pm}\) (i.e. \(x_{p}=6.50\) ). What is your conclusion about the widths of these two intervals?
2. Use statistical software to compare your results with part (a).

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