A linear regression equation of best fit between a student's attendence and the degree of sucess in school is h = 0.5x + 68.5. the correlation coefficent, r, for these data would be
(1) 0 < r < 1
(2) -1< r < 0
(3) r = 0
(4) r = -1
is the answer no. 1?
You've got a positive relationship (perhaps not surprisingly) between attendance and success, which you can see from the sign of the coefficient on the X term (+0.5). That means the correlation coefficient (which can only lie between -1 and +1) is positive. Only one of the four possible answers describes that situation.
Yes, it is.
thanks
Well, I would say that if a student's attendance is positively correlated with their degree of success in school, then the correlation coefficient, r, would be (1) 0 < r < 1. Just like how showing up to a party increases your chances of having a good time!
To determine the correlation coefficient (r) for a linear regression equation, you need to know the slope (0.5) and the nature of the relationship between the variables.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where -1 indicates a strong negative linear relationship, 0 indicates no linear relationship, and 1 indicates a strong positive linear relationship.
In this case, the slope of the linear regression equation is positive (0.5), which suggests a positive relationship between a student's attendance and degree of success in school. However, the value of the correlation coefficient (r) cannot be determined solely from the slope of the equation.
To find the correlation coefficient (r), you would need additional information, such as the standard deviations of the attendance and success variables, and the covariance between the two variables. With this information, you can calculate the correlation coefficient using the formula:
r = (cov(x, y)) / (σx * σy)
Therefore, without further information, it is not possible to determine the exact value of the correlation coefficient (r) for the given equation. Thus, none of the given options (1), (2), (3), or (4) are valid choices.