In simple regression analysis, if the correlation coefficient is a positive value, then select one:

a. the slope of the regression line must also be positive.

b. the least squares regression equation could have either a positive or a negative slope.

c. the y-intercept must also be a positive value.

d. the coefficient of determination can be either positive or negative, depending on the value of the slope.

e. the standard error of estimate can have either a positive or a negative value.

When using simple regression, if the correlation coefficient is a positive value,  A. the slope of the regression line must also be positive.

The correlation coefficient shows the change in y as a result of a change in x. When this figure is positive, it means that the change in y is positive when there is a change in x.

This will then be represented graphically as a positive slope because the correlation coefficient is the mathematical representation of the slope.

In conclusion, the slope of a regression line will be positive when the correlation coefficient is positive.

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check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.