The following 54 pairs of data give, for Old Faithful geyser, the duration in minutes of an eruption and the time in minutes until the next eruption:

(a) Calculate the correlation coefficient, and construct a scatterplot, of these data.
(b) To estimate the distribution of the correlation coefficient, R, resample 500 samples of size 54 from the empirical distribution, and for each sample, calculate the value of R.
(c) Construct a histogram of these 500 observations of R.
(d) Simulate 500 samples of size 54 from a bi-variate normal distribution with correlation coefficient equal to the correlation coefficient of the geyser data. For each sample of 54, calculate the correlation coefficient.
(e) Construct a histogram of the 500 observations of the correlation coefficient.
(f) Construct a q€“q plot of the 500 observations of R from the bi-variate normal distribution of part (d) versus the 500 observations in part (b). Do the two distributions of R appear to be about equal?

Transcribed Image Text:

(2.500, 72) (4.467, 88) (2.333, 62) (5.000, 87) (1.683, 57) (4.500, 94) (4.500, 91) (2.083, 51) (4.367,98 (1.583, 59) (4.500, 93) (4.550, 86) (1.733, 70) (2.150, 63) (4.400, 91) (3.983, 82) (1.767, 58) (4.317, 97) (1.917, 59) (4.583, 90) (1.833, 58) (4.767, 98) (1.917,55) (4.433, 107) (1.750, 61) (4.583, 82) (3.767,91) (1.833, 65) (4.817, 97) (1.900, 52) (4.517, 94) (2.000, 60) (4.650, 84) (1.817, 63) (4.917,91) (4.000, 83) (4.317, 84) (2.133, 71) (4.783, 83) (4.217,70) (4.733, 81) (2.000, 60) (4.717,91) (1.917,51) (4.233, 85) (1.567, 55) (4.567, 98) (2.133, 49) (4.500, 85) (1.717, 65) (4.783, 102) (1.850, 56) (4.583, 86) (1.733, 62)