The problem provided involves determining the correlation coefficient for a regression analysis where the relationship between temperature (independent variable) and fish activity (dependent variable) is analyzed.

Step 1: Relationship between $R^2$ and the Correlation Coefficient

The coefficient of determination, $R^2$, is related to the correlation coefficient $r$ by: $r = \pm \sqrt{R^2}$ The sign of $r$ depends on the slope (or coefficient) of the independent variable in the regression model. In this case, the coefficient of temperature is negative ($-3.21667$), so $r$ will be negative.

Step 2: Calculate $r$

From the given table, $R^2 = 91\% = 0.91$. Thus: $r = -\sqrt{0.91}$ $r \approx -0.954$

Step 3: Answer the Question

The correct answer is:

• About -0.954

Would you like me to explain any specific part of this calculation or explore any related topics further?

Expanding the Context:

1. What does the negative sign of the correlation coefficient indicate in this case?
2. How is the t-ratio used to evaluate the significance of the temperature coefficient?
3. What does the $R^2$ value tell us about the strength of the model's fit?
4. Why is the adjusted $R^2$ slightly lower than $R^2$, and when is adjusted $R^2$ more relevant?
5. How does the F-ratio support the significance of the regression model?

Tip:

Always consider the slope and direction of the relationship when interpreting the sign of the correlation coefficient.