Question

In the equation of trend line \(y_t=a+bx\), a and b represent:

• A. the mean of y and the slope of trend line respectively
• B. the slope of trend line and the mean of y respectively
• C. the mean of xy and the slope of tend line respectively
• D. the slope of trend line and the mean of x respectively

Answer 1

The Correct Option is A

In the equation of the trend line \(y_t=a+bx\), it is essential to understand what a and b represent. The equation is a form of a linear regression model where:

• a: This is the y-intercept of the trend line, which represents the average (mean) value of the dependent variable y when the independent variable x is zero. Therefore, a represents the mean of y.
• b: This is the slope of the trend line. It indicates the change in the dependent variable y for every one-unit change in the independent variable x. Thus, b is the slope of the trend line.

Given this understanding, the correct interpretation of a and b in the context of the trend line equation is as follows:

• The mean of y and the slope of trend line respectively.