Question

In: Statistics and Probability

The following ANOVA table was obtained when estimating a multiple regression model. ANOVA df SS MS...

The following ANOVA table was obtained when estimating a multiple regression model.


ANOVA df SS MS F Significance F
   Regression   2 188,246.80    94,123.40    35.2     9.04E-07      
   Residual 17   45,457.32    2,673.96   
   Total 19   233,704.10   


a. Calculate the standard error of the estimate. (Round your answer to 2 decimal places.)
  se   
b-1. Calculate the coefficient of determination. (Round your answer to 4 decimal places.)
  Coefficient of determination   


b-2. Interpret the coefficient of determination.
  
The proportion of the variation in y that is explained by the regression model.
The proportion of the variation in x that is explained by the regression model.
  c. Calculate adjusted R2. (Round your answer to 4 decimal places.)
  Adjusted R2   

Solutions

Expert Solution

Part a) :

The standard error of the estimate= Se = SQRT( MS of Residual /Df of Resudual .)

MS of residual = 2673.96   and df of residual = 17 .

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Part b)-1 ) Calculate the coefficient of determination.

Coefficient of determination denoted by , R2

Formula for R2 = SS Regression /SS total .

Coefficient of determination denoted by , R2 = 0.8055

b-2. Interpret the coefficient of determination.

The proportion of the variation in y that is explained by the regression model.

------------------------

Part c ) Calculate adjusted R2.

         p= number of parameter , N= total sample size

df for Regerssion =p - 1 and here df for regression is as 2

So , p - 1 = 2 ==>>>p = 3

And df for total =N-1   and here df for total =19 .

So , N-1 = 19 ==>>N= 20 .


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