Numa regressão linear simples, verificou-se um coeficiente d...

Obtido com ChatGPT:

The determination coefficient, also known as the coefficient of determination, is a statistical measure that represents the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It is denoted by the symbol R^2 and takes on values between 0 and 1.

The correlation coefficient, on the other hand, is a measure of the strength and direction of the linear relationship between two variables. It is denoted by the symbol r and also takes on values between -1 and 1.

There is a connection between the determination coefficient and the correlation coefficient. Specifically, the determination coefficient is equal to the square of the correlation coefficient (R^2 = r^2). This means that if you know the correlation coefficient between two variables, you can determine the proportion of variance in the dependent variable that is predictable from the independent variable(s) by squaring the correlation coefficient. For example, if the correlation coefficient between two variables is 0.8, the determination coefficient is 0.64 (0.8^2 = 0.64).

GABARITO D

(R) Coeficiente de correlação = 0,756

(R2) Coeficiente de determinação = 0,756 x 0,756 = 0,57..

Na regressão linear simples, o coeficiente de correlação (r) é um número que indica o grau de correlação linear entre as variáveis X e Y.

Já o coeficiente de determinação (R2) é uma medida de qualidade do ajuste do modelo.

Ocorre que o R2 é justamente o quadrado do r.

Como a questão fornece r=0,756, teremos:

R2=0,756^2≈0,57

Gabarito: Letra D.

Se perguntar sobre *coeficiente de determinação* é só pegar o coeficiente de correlação da amostra e multiplicar o número por ele mesmo.

Assim:

0,756 x 0,756 = 0,571536