Question

date:
period:
scatterplots & trend lines

1. what is the relationship of the graph below? (positive, negative, no relationship)

1. draw a trend line for the points in the scatter graph.

1. use the line to predict the value of y when x = 12.

1. what could be the y-intercept of the trend line?

Explanation:

Question 1

Step1: Analyze scatterplot trend

Observe the scatterplot points. As \( x \) (horizontal axis) increases, \( y \) (vertical axis) values generally increase.

Step2: Determine relationship type

A positive relationship exists when \( y \) increases with \( x \), negative when \( y \) decreases with \( x \), and no relationship if points are random. Here, the trend is upward with increasing \( x \), so it's positive.

Question 2

Step1: Identify trend direction

From Question 1, we know the trend is positive, so the trend line should have a positive slope.

Step2: Draw the line

Place the line such that about half the points are above and half below, aligning with the upward pattern of the scatterplot points.

Question 3

Step1: Locate \( x = 12 \) on the x - axis

Find the vertical line corresponding to \( x=12 \) on the graph.

Step2: Find intersection with trend line

Draw a vertical line at \( x = 12 \) and find where it intersects the trend line. Then, read the \( y \) - value from the y - axis at that intersection point. Based on the general upward trend and the distribution of points, the \( y \) - value is around 6.

Question 4

Answer:

positive