Question

In the regression equation, y = 49.56 + 0.97x, the slope is _______.

Answer 1

m = 0.97

Step-by-step explanation:

1. Reference the equation of a line:
`y=mx+b`.

2. The equation given has the same relative structure of the normal equation of a line. However, it is organized just slightly different. Compared to the normal equation, the equation written to us is in the form of
`y=b+mx`.

3. When the equation is not in the same exact form and organization but still has somewhat similar structure (y is isolated, all variables are simplified), then we can identify the slope by seeing what number is attached to x. In this case, 0.97 has an x attached, therefore that is the slope.

Answer 2

The slope in the regression equation y = 49.56 + 0.97x is 0.97. It describes how y is expected to change with each one unit increase in x.

Step-by-step explanation:

In the regression equation y = 49.56 + 0.97x, the slope is represented by the coefficient of the x variable. In this equation, the coefficient or the slope is 0.97. This means for every one unit increase in the independent variable x, the dependent variable y increases by 0.97. It is important to note that the slope is defined as the rise divided by the run and reflects how steep the line is on a graph. The slope can indicate the strength of the relationship between the two variables, with a positive slope indicating a positive relationship.

The y-intercept is the other component of the linear equation and is represented by b, which in this case is 49.56. The y-intercept is the point at which the line crosses the vertical axis when x is zero.