Using a graphing calculator to find the line of best fit for

Using a graphing calculator to find the line of best fit for the data below.   Tell whether there is a strong correlation between the data:   x (3,7,5,4,6,20,15,12)    y (1,8,-1,5,10,18,20,-6)

I am checking my work against yours, please list all steps used. Thanks.

Solution

a. Line of best Fit

Mean of X = X / n =    9
Mean of Y = Y / n =   6.875
(Xi - Mean)^2 =   256
(Yi - Mean)^2 =   572.88
(Xi-Mean)*(Yi-Mean) =   227
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = 227 / 256 = 0.8867  
bo = Y / n - b1 * X / n  
bo = 6.875 - 0.8867*9 = -1.1055  
  
Y = bo + b1 X  
  
Y\'=-1.1055+0.8867*X  

b. correlation between the data

r( X,Y) =    Co V ( X,Y) / S.D (X) * S.D (y)                      
r( X,Y) =    Sum(XY) / N- Mean of (X) * Mean of (Y) / Sqrt( X^2/n - ( Mean of X)^2 ) Sqrt( Y^2/n - ( Mean of Y)^2 )                        
                          
Co v ( X, Y ) =   1 /8 (722) - [ 1/8 *72 ] [ 1/8 *55] =            28.375          
S. D ( X ) =   Sqrt( 1/8*904-(1/8*72)^2)           5.657          
S .D (Y) =    Sqrt( 1/8*951-(1/8*55)^2)           8.462          
r(x,y) =    28.375 / 5.657*8.462   =   0.5928              
                          
If r = 0.5928> 0 ,Perfect Positive Correlation