Question

Compute the regression equation (regression coefficient and constant) using data

Given X: Mean = 14; Variance = 8.667; Std Deviation = 2.944. Y: Mean = 13; Variance = 86.667; Std Deviation = 9.309.

cross products = 18, 45, 4 , -9, 4, -3, 52.

covariance = 15.857143

Correlation = 0.578608

X - u   Y - u

      -3       -6

  -3      -15

   -2                -2  

      -1       9

     2              2    

     3         -1

       4 13

. Compute the explained variance (R Square) and the standardized regression coefficient (beta) for this model. For R Square, Sums of Squares Explained = 235.944; Sums of Squares Total = 520.

Please explain and type the answer as i want to copy it.

Answer 1

a) R² or the coefficient of determination is computed as the proportion of total variation in the dependent variable that is explained by the independent variable variation or explained by regression. Therefore, it is computed here as:

therefore 0.4537 is the required value here.

b) The value of the slope coefficient here is computed as:

Therefore 1.8296 is the required value of the standardized regression coefficient for the model here.