Explanation:

When the correlation coefficient between two variables is 1, it means that there is a perfect positive linear relationship between the two variables. In other words, as one variable increases, the other variable also increases in a perfectly linear manner.

When the correlation coefficient is 1, it implies that the two lines of regression for the variables are coincident. This means that the lines representing the regression equations for the variables will overlap each other.

Regression Line:
A regression line is a line that represents the relationship between two variables. In simple linear regression, the regression line is represented by the equation:
y = mx + b
where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Explanation of Options:
a) Parallel: When the correlation coefficient is 1, the lines of regression are not parallel. They are coincident, as mentioned earlier.
b) At right angles: When the correlation coefficient is 1, the lines of regression are not at right angles to each other. This condition occurs when the correlation coefficient is 0, indicating no linear relationship.
c) Coincident: This is the correct answer. When the correlation coefficient is 1, the lines of regression for the two variables are coincident, meaning they are the same line.
d) None of these: This option is incorrect because the lines of regression are indeed coincident when the correlation coefficient is 1.

Conclusion:
In conclusion, when the correlation coefficient between two variables is 1, the lines of regression for the variables are coincident. This means that the lines representing the regression equations for the variables will overlap each other.