Question

1. in linear regression, what is the best - fit line?

a. a curved line that connects all the data points.
b. the line that comes closest to all the data points on a graph.
c. the line that is furthest away from all the data points on a graph.
d. a line that only connects the first and last data points.

1. what does x represent in the linear regression equation y = a + bx?

a. how steep the line is.
b. the value we already know.
c. the value we are trying to predict.
d. the starting point of the line.

1. according to the passage, what is one important consideration before using linear regression?

a. the data must be collected over at least one year.
b. the data must be perfectly linear with no variation.
c. one of the variables must be time.
d. the two variables being analyzed should have a relationship.

Explanation:

1. In linear regression, the best - fit line is the line that minimizes the sum of the squared distances between the line and all the data points on a graph, so it comes closest to all the data points.
2. In the linear regression equation $Y = a + bX$, $X$ is the independent variable, which is the value we already know and use to predict $Y$.
3. For linear regression to be applicable, the two variables being analyzed should have a linear relationship.

Answer:

1. B. The line that comes closest to all the data points on a graph.
2. B. The value we already know.
3. D. The two variables being analyzed should have a relationship.