Question

Consider the following general model (for a random draw, i, from the population), where a¡ is the intercept for unit i and by is the slope:

y = a + bᵢxᵢ
With a random sample of size n, we implicitly draw a values of b; along with a values of a; (and the observed data on x and y). In this model, __________can be estimated.

O the average slope and average intercept
O slope and intercept

Answer 1

The average slope and average intercept can be estimated from a random sample in a linear model. The slope represents the relationship between two variables, and the intercept is where the line crosses the y-axis.

Step-by-step explanation:

In the model y = a + bixi, the average slope and average intercept can be estimated with a random sample of size n. When we collect data on x and y, the slope and intercept can be estimated from this sample, where the slope, represented by b, describes the steepness of the line, and the intercept, represented by a, indicates the point where the line crosses the y-axis.

To estimate the population standard deviation of y using the standard deviation of the residuals, the formula s = SSE/n-2 is used.

For example, in the context of economics, the slope is very useful because it quantifies the relationship between the independent variable (x) and the dependent variable (y), providing an average effect of a one-unit increase in x on y.

The model in question is represented by the equation y = a + bixi, where a represents the y-intercept and bi represents the slope. In this model, slope and intercept can be estimated.

The slope, b, indicates the rate of change of the dependent variable (y) for every one unit increase in the independent variable (x). The y-intercept, a, represents the value of y when x=0.