Question

True or false?:

1) If X and Y are standardized, then fit a linear regression line of standardized Y on standardized X, correlation between X and Y equals the slope of regression line.

2) If one calculates r for a set of numbers and then adds a constant to each value of one of the variables, the correlation will change.

3) The easiest way to determine if a relationship is linear is to calculate the regression line.

4) If the relationship between 2 variables is perfect the standard error of estimate equals 0.

Answer 1

1. We know, = .

If X and Y are standardized, then, = = 1.

So, = r.

Hence, the given statement is True. (Ans).

2. Let r = Cor(X, Y) = Cov(X, Y) / ,

Now, for some constants a and b, Cor(X + a, Y + b) = Cov(X + a, Y + b)/.

Cov(X + a, Y + b) = Var(X + a + Y + b) - Var(X + a) - Var(Y + b) = Var(X + Y) - Var(X) - Var(Y) = Cov(X, Y)

So, Cor(X + a, Y + b) = Cor(X, Y).

Hence, the given statement is False. (Ans).

3. The easiest way is to plot the dependent variable against the independent variable. Hence, the given statement is False. (Ans).

4. Perfect relationship ensures between two variables ensure that the standard error of estimate equals 0. Hence, the given statement is True. (Ans).