A study using satellites recorded the mass of ice and the number of lightning fl

Question

A study using satellites recorded the mass of ice and the number of lightning flashes per minute in thunderstorm cells over a particular region of the country. Prior to analyzing the data, the researchers transformed both variables using logarithms (base 10). They then performed a linear regression of log(y) on log(x), where x = ice mass (in kg) and y = number of lightning flashes per minute. The least squares regression line of log(y) on log (x) resulting from the regression analysis was predicted value of log (v) = -0.285 + 0.2255 log(x). What does the model predict for the number of lightning flashes per minute when the ice mass is 66.000.000 kg? (A) 2.1 (B) 5.9 (C) 16.8 (D) 23.8 (E) 30.1

Explanation / Answer

Given:

log y = - 0.285 + 0.2255 log x               (1)

where

x = ice mass (in kg)

y = number of lightning flashes per minute

Givrn:

x = 66000000

To find y:

Substituting in (1), we get:

log y = - 0.285 + 0.2255 X log (66000000)

         = - 0.285 + 0.2255 X 7.8195

         = - 0.285 + 1.7633

         = 1.4783

So,

y = 30.1

So,

Correct option is:

(E) 30.1

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