Statistical Regression Estimation

Explanation

In a univariate regression, the correlation coefficient is the square root of the R-square. Hence, correlation coefficient = sqrt(0.63) = 0.79

To determine the correlation coefficient between the dependent and independent variables based on the given information, we can use the relationship between the coefficient of determination (R-square) and the correlation coefficient.

The coefficient of determination (R-square) is a measure of how well the independent variable(s) explain the variation in the dependent variable. It represents the proportion of the total variation in the dependent variable that can be explained by the independent variable(s).

In this case, the R-square is given as 63%. This means that 63% of the total variation in the dependent variable is explained by the independent variable(s).

The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. A positive correlation coefficient indicates a positive linear relationship, while a negative correlation coefficient indicates a negative linear relationship.

The relationship between R-square and the correlation coefficient is given by the formula: R-square = (correlation coefficient)^2

We can rearrange this formula to solve for the correlation coefficient: correlation coefficient = sqrt(R-square)

Using the given R-square of 63%, we can calculate the correlation coefficient as follows: correlation coefficient = sqrt(0.63) = 0.79

Therefore, the correlation coefficient between the dependent and independent variables is 0.79.

The correct answer is D. 0.79.