14. The accompanying data are x = advertising share and y = market share for a p

Question

14. The accompanying data are x = advertising share and y = market share for a particular brand of cigarettes during 10 randomly selected years.

(a) Calculate the equation of the estimated regression line. (Round your answers to six decimal places.)
y =

Obtain the predicted market share when the advertising share is 0.09. (Round your answer to five decimal places.)
2

(b) Compute r2. (Round your answer to three decimal places.)
3

(c) Calculate a point estimate of . (Round your answer to four decimal places.)
4

On how many degrees of freedom is your estimate based?
5

x 0.101 0.072 0.071 0.077 0.086 0.047 0.060 0.050 0.070 0.052 y 0.133 0.128 0.121 0.086 0.079 0.076 0.065 0.059 0.051 0.039

Explanation / Answer

  
Mean of X = X / n =    0.0686
Mean of Y = Y / n =   0.0837
(Xi - Mean)^2 =   0.0026
(Yi - Mean)^2 =   0.01
(Xi-Mean)*(Yi-Mean) =   0.0034
b1 = (Xi-Mean)*(Yi-Mean) / (Xi - Mean)^2    
b1 = 0.0034 / 0.0026 = 1.3077  
bo = Y / n - b1 * X / n  
bo = 0.0837 - 1.3077*0.0686 = -0.006  
  
Y = bo + b1 X  
  
Y'=-0.006+1.3077*X  

2.

To obtain market share when advertising share is 0.09 then
Y'= -0.006+1.3077*0.09= 0.111693

3.

   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 /12 (309.060676) - [ 1/12 *182.686 ] [ 1/12 *4.237] = 20.38                              
   S. D ( X ) = Sqrt( 1/12*16564.049664-(1/12*182.686)^2) = 33.891                              
   S .D (Y) = Sqrt( 1/12*5.939955-(1/12*4.237)^2) = 0.609                              
   r(x,y) = 20.38 / 33.891*0.609 = 0.9874                              
                                  
   If r = 0.9874> 0 ,Perfect Positive Correlation                              
                                  
   Coeffcient of determination = r^2 = 0.974959                              
                                  

Line of Regression Y on X i.e Y = bo + b1 X X Y (Xi - Mean)^2 (Yi - Mean)^2 (Xi-Mean)*(Yi-Mean) 0.101 0.133 0.001 0.0024 0.0016 0.072 0.128 0 0.002 0.0002 0.071 0.121 0 0.0014 0.0001 0.077 0.086 0.0001 0 0 0.086 0.079 0.0003 0 -0.0001 0.047 0.076 0.0005 0.0001 0.0002 0.06 0.065 0.0001 0.0003 0.0002 0.05 0.059 0.0003 0.0006 0.0005 0.07 0.051 0 0.0011 0 0.052 0.039 0.0003 0.002 0.0007

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