Find the mean and standard deviation of the times and icicle lengths for the dat

Question

Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data391.dat. Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Use the same five numbers to find the equation of the regression line for predicting the time an icicle has been growing from its length. (Round your answers to three decimal places.)

Time on top

Length on bottom

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 2.2 .7 3.8 6.1 7.4 7.7 8.7 13.1 14 17.5 16.2 20.5 22.3 22.1 25.4 26.9 28 30

Explanation / Answer

Times x (mean) = 95

Times s = 53.59

lengths x = 15.14

lengths s = 9.44

Correlation r = 0.993

For predicting time from length

Slope, b = r*standard deviation of time/ standard deviation of length = 0.993*(5.38/9.43) = 5.62

a = mean of time - b* mean of length = 95 - 5.62*15.14 = 9.9

So, regression equation is

time = 9.9 + 5.62*length

For predicting length from time

Slope, b = r*standard deviation of length/ standard deviation of time = 0.993*(9.435/53.38) = 0.176

a = mean of length - b* mean of time = 15.15 - 0.176*95 = -1.53

So, regression equation is

length = -1.526 + 0.176*time

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