5. The regression line can be used to predict the value of the independent variable (x).

Question

5. The regression line can be used to predict the value of the independent variable (x).

A) True B) False

true??

Answer 1

if

y = f(x)
the independent value is x and the dependent value is y
When you observe a bunch or y values for values of x, like for example height (y) versus age (x) then you generally graph x on the horizontal axis and y up from the horizontal axis. That means that you have a bunch of heights associated with each age.
You suppose that height depends on age, so you fit a line (or a parabola or whatever) as best you can through the points. The formal process is called "regression".
Now for any age (x) , you can make a good guess at height(y). However there may be several values of height (y) for each value of age (x) you used. It would not be safe to guess age from the height therefore although you could have done the whole process backwards and graphed x as a function of y fitting your line through the age points instead of the heights . I would therefore say false, although I could turn he whole problem around :)

Answer 2

By the way if I turned it around that would be doing the "inverse" problem. Obviously given the height I could guess the age, but that is the inverse of the way you set this regression problem up.

Answer 3

Yes, that is correct. The regression line, also known as the line of best fit, is a statistical tool used to model the relationship between two variables, typically referred to as the independent variable (x) and the dependent variable (y). One of the main purposes of the regression line is to make predictions about the values of the dependent variable based on known values of the independent variable. So, the statement "The regression line can be used to predict the value of the independent variable (x)" is true.