Question

formula of correlation coefficient of multiple regression

Answer 1

The formula for the correlation coefficient (r) of multiple regression can be calculated using the following steps:

1. Calculate the predicted values (Y') for each observation using the multiple regression equation:
Y' = b0 + b1*X1 + b2*X2 + ... + bn*Xn
Where b0, b1, b2, ..., bn are the regression coefficients and X1, X2, ..., Xn are the predictor variables.

2. Calculate the sum of squares total (SST) using the formula:
SST = Σ((Y - Ȳ)^2)
Where Y is the observed dependent variable and Ȳ is the mean of the observed dependent variable.

3. Calculate the sum of squares regression (SSR) using the formula:
SSR = Σ((Y' - Ȳ)^2)

4. Calculate the sum of squares error (SSE) using the formula:
SSE = Σ((Y - Y')^2)

5. Calculate the correlation coefficient (r) of the multiple regression using the formula:
r = √((SSR / SST))

Note: The correlation coefficient (r) ranges from -1 to +1, where -1 indicates a perfect negative relationship, +1 indicates a perfect positive relationship, and 0 indicates no relationship between the variables.