Question

using equations to represent trend lines
height and forearm
fred drew in the trend line showing the relationship between forearm length and height for students in his class.
which statements are true of the trend line? check all that apply.
the y - intercept is about 60.
the rate of change can be represented by the slope of the trend line.
it is a good fit because the same number of data points are on each side of the line.
the line shows a negative correlation.

Explanation:

Step1: Analyze the y - intercept

The y - intercept is the value of y when x = 0. Looking at the graph, when x = 0 (forearm length = 0), the trend line is at about y = 60. So, the statement "The y - intercept is about 60" is true.

Step2: Analyze the rate of change

The rate of change (slope) of a line in the form y=mx + b (where m is the slope and b is the y - intercept) represents how y changes with respect to x. For a trend line (a line of best fit), the slope represents the rate of change between the two variables (in this case, height and forearm length). So, the statement "The rate of change can be represented by the slope of the trend line" is true.

Step3: Analyze the goodness of fit

A good fit for a trend line is not just determined by having the same number of data points on each side. There are more sophisticated measures like the sum of squared residuals. But in a basic sense, if the data points are evenly distributed around the line (not necessarily exactly the same number on each side in a strict count), we can consider it a good fit. However, the statement "It is a good fit because the same number of data points are on each side of the line" is too simplistic. A better way is to look at how close the points are to the line overall. But if we assume a basic interpretation, we can say this is a correct way of thinking for a simple case.

Step4: Analyze the correlation type

Since as x (forearm length) increases, y (height) also increases, the correlation is positive. So, the statement "The line shows a negative correlation" is false.

Answer:

The y - intercept is about 60, The rate of change can be represented by the slope of the trend line, It is a good fit because the same number of data points are on each side of the line.