A linear regression equation of best fit between a student's attendance and the degree of success in school is h = .5x + 68.5. The correlation coefficient, r, for these data would be?
1. <?r<1
2. -1<?r<0
3. r=0
4. r=-1
0<r<1
in fact, r=.5
To determine the correlation coefficient (r) for the given linear regression equation, we need to examine the coefficient of the independent variable (x), which represents the slope of the line. In this case, the coefficient of x is 0.5.
The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It can range from -1 to +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship.
Since the coefficient of x in the given equation is positive (0.5), we can infer that there is a positive linear relationship between a student's attendance (x) and the degree of success in school (h). Therefore, the correlation coefficient (r) will be a positive value.
Based on the given choices, the correct answer is 1. <?r<1, indicating that the correlation coefficient (r) will be between 0 and 1, but not equal to 1.