Question

1. True or False: A correlation of 1.0 implies a perfect positive correlation.

2. True or False: The fact that two variables are correlated does not mean that one causes the other.

3. True or False: The value of the correlation (r) between X and Y does not change if all values of X are multiplied by 100.

4. True or False: The Covariance between two variables has a range from -1.0 to 1.0.

5. True or False: A correlation of zero means there is no linear relationship between the two variables.

6. True or False: In a bivariate regression (single independent variable) the intercept coefficient is the value of the dependent variable when the independent variable equals zero.

Answer 1

Solution:

1) A correlation of 1.0 implies a perfect positive correlation.

True.

Correlation coefficient is between -1 to + 1. r = -1 represents perfect negative , r = 0 represents no correlation and r = +1 represents perfect positive correlation.

Thus answer is True.

2) The fact that two variables are correlated does not mean that one causes the other.

True

If there is causal relationship between two variables, then variables are correlated but it is not always true that if variables are correlated then there is causal relationship.

3) The value of the correlation (r) between X and Y does not change if all values of X are multiplied by 100.

True

Since correlation coefficient is ratio of covariance to the product of standard deviation of X and Y, thus change of scale affects on covariance and standard deviations but it cancels due to ratio of covariance to the product of standard deviation of X and Y. Hence The value of the correlation (r) between X and Y does not change if all values of X are multiplied by 100.

4) The Covariance between two variables has a range from -1.0 to 1.0.

False

Since covariance is average of product of deviations of X values and Y values from their respective means and thus deviations can be negative or positive , but these deviations takes values depending on values in data set.

If data has large values, then covariance would be larger ( negative or positive)

If data has small values , then covariance would be smaller ( negative or positive)

Thus it can be anything between minus infinity to plus infinity.

5) A correlation of zero means there is no linear relationship between the two variables.

True.

6) In a bi-variate regression (single independent variable) the intercept coefficient is the value of the dependent variable when the independent variable equals zero.

True.

General regression equation is:
y = a + bx

a = intercept

b = slope

if x = 0

then y = a + b*0

y = a + 0

y = a = intercept.