Question

The accompanying data contains the depth (in kilometers) and magnitude, measured using the Richter Scale, of all earthquakes in a particular region over the course of a week. Depth is the distance below the surface at which the earthquake originates. A one unit increase in magnitude represents ground shaking ten times as strong - an earthquake with magnitude 4 is ten times as strong as an earthquake with magnitude 3.

Depth	Magnitude
9.069.06	2.732.73
2.912.91	2.732.73
6.566.56	1.051.05
2.712.71	1.891.89
2.362.36	1.891.89
2.212.21	0.420.42
5.665.66	1.471.47
6.216.21	0.210.21

For computation purposes,
?¯x¯ = 4.71 , ?¯y¯ = 1.54875 , ∑?∑x= 37.68 , ∑?∑y = 12.39 , ∑??∑xy = 59.7009 , ∑?2∑x2 = 221.9828 , ∑?2∑y2 = 25.5339 ,

Using depth as the explanatory variable ?x, compute the correlation coefficient and then find the regression line.

The correlation coefficient is ?=r=  . (Round to 4 decimal places.)

The equation of the least squares line is
?̂ =y^=  +  x. (Round to 4 decimal places.)

Answer 1

	X	Y	XY	X²	Y²
total sum	37.680	12.390	59.70	221.983	25.53
mean	4.7100	1.5488

sample size ,   n =   8          
here, x̅ =Σx/n =   4.7100   ,   ȳ = Σy/n =   1.54875  
                  
SSxx =    Σx² - (Σx)²/n =   44.510          
SSxy=   Σxy - (Σx*Σy)/n =   1.344          
SSyy =    Σy²-(Σy)²/n =   6.345         

correlation coefficient ,    r = Sxy/√(Sx.Sy) =   0.0800

...................

estimated slope , ß1 = SSxy/SSxx =   1.344   /   44.510   =   0.0302
                  
intercept,   ß0 = y̅-ß1* x̄ =   1.4065          
                  
so, regression line is   Ŷ =   1.4065   +   0.0302   *x

.....................

THANKS

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