Question

How do you interpret the slope of a linear regression?

Answer 1

Hint:
Given a linear regression model. We have to find the slope of the linear regression. First, we will determine the x and y coordinates of the line for two points on the line. Then, we will determine the difference of y values and difference in x values. Then, divide the change in y values by change in x values.

Complete step by step solution:
The regression line is represented by a linear equation which defines the relationship between two variables. For example, \[y = a + bx\]
One variable is known as an explanatory variable and the other variable is dependent variable.
Here, x is an explanatory variable and y is a dependent variable.
The slope of the line always represents the steepness of the line which defines the average rate of change of line. As the magnitude of slope increases, the steepness of the line also increases.
For example, consider the equation \[y = 7 + 2x\]
Here, the slope of the line is positive that is 2, which means when the value of x increases by 1 unit, the value of y increases by 2.
Consider, \[y = 7 - 2x\]
Here, the slope of the line is negative, that is \[ - 2\], which means when the value of x increases by 1 unit, the value of y decreases by 2 units.
Also, consider the linear regression line equation, \[y = - 3\].
Here, the slope of the line is zero because the line is neither increasing nor decreasing.

Final answer: Hence the slope defines the change in y value according to the x value.

Note:
Please note that in such types of questions students can draw the graph of linear regression equation to easily determine whether the slope is positive, negative or zero.