Joe Bob observes a correlation of r=0.50 between number of flowers in a garden a

Question

Joe Bob observes a correlation of r=0.50 between number of flowers in a garden and the number of butterflies which appear in traps set out in that garden to capture and estimate the butterfly population. He has observed this is a sample of 100 gardens. He also notes that the Standard Deviation (SD) of the number of flowers is about twice as large as the SD of the butterfly count in his sample.   

He wants to use this relationship to predict how many butterflies he can expect to see in his own flower garden, but he doesn't know how to find the slope of the regression line.

Help Joe Bob out. What is the estimated slope, based on his sample of 100 flower gardens, given the information he has?   

Please give steps with brief explanations! Thank you.

Explanation / Answer

Dependnet variable Y=butterfly count

Independnt variable X=number of flowers

Slope=r*sy/sx

We have r=0.50 and sx=2*sy

So slope= 0.50*1/2=0.25

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