Question

1. The following data give the times (in seconds) of 22 male swimmers who entered the 50 yard freestyle race in the conference championship meet, where Xis the swimmer's best time for the season and Y is the swimmer’s time in the meet.

X	Y	X	Y	X	Y	X	Y
24.97	23.98	24.76	23.63	23.80	23.61	22.84	23.58
24.07	23.57	22.98	23.17	22.93	22.83	23.41	22.75
22.10	22.74	23.08	22.70	23.59	22.62	23.80	22.53
22.38	22.39	22.91	22.34	22.08	21.95	22.46	21.73
21.34	21.68	22.76	21.66	21.82	21.68	21.80	21.58
22.26			21.35

Σ?_? = 503.50,         Σ?_? = 495.64,         Σ?_?² = 11544.18,         Σ?_?² = 11180.06, Σ?_??_? = 11357.41.

1. To predict the performance of a swimmer at the meet based on his season’s best time, a simple linear regression model is fitted to the data. Find the least square regression line, and interpret.
2. Find a 95% confidence interval for the slope parameter of the regression line. Interpret your results.
3. Find a 95% prediction interval for the time in the meet of a swimmer whose season’s best time is 21.5 seconds.
4. Find a 95% confidence interval for the mean time of all male swimmers whose season’s best time is 21.5 seconds.

Answer 1