How do you find the trend line?

study.com - What is a Trend Line? - Video & Lesson Transcript - Study.com

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Interpreting a Trend Line

How does someone interpret or understand a trend line? Recall that a trend line can help find a pattern, if one exists, in the relationship between two variables. Looking at the direction of the trend line helps to clarify the directions of the association between the variables: A trend line with a positive slope indicates a positive relationship between the variables. They increase or decrease together. indicates a positive relationship between the variables. They increase or decrease together. A trend line with a negative slope indicates a negative relationship between the two variables. When one goes up, the other goes down, and vice versa. indicates a negative relationship between the two variables. When one goes up, the other goes down, and vice versa. A trend line with a slope of 0, which is a horizontal line, indicates a constant relationship between the two variables. No matter which direction one goes, the other stays the same. Do all relationships have a trend line? No, all relationships do not have a trend line. Trend lines are generally constructed from scatter plots. What is a scatter plot? A scatter plot is a graph where the relationship between two variables is plotted in a set of points. These points may or may not show a trend. This scatter plot shows the number of letters in a person's first name on the x-axis and the number of cups of water the person drank yesterday on the y-axis.

Scatter plot with no trend

The scatter plot shown does not show a trend. The points are not in any sort of pattern, but rather scattered around randomly. There is no trend or pattern in the number of letters in a person's first name and the number of cups of water the person drank yesterday.

Positive Trend Graph

A positive trend graph is a graph in which the trend line has a positive slope. This indicates a positive relationship between the variables, which means they increase or decrease together. This graph shows the relationship between the total income level of a person and the amount the person pays in federal income taxes.

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Positive trend graph

As the total income level of the person increases, the amount the person pays in federal income taxes also increases. This is an example of a positive trend graph. There are some fluctuations in the values, but the overall trend is a positive one. The estimated trend line for this graph has a positive slope.

Negative Trend Graph

A negative trend graph is a graph in which the trend line has a negative slope. This indicates a negative relationship between the variables, which means when one goes up, the other goes down, and vice versa. This graph shows the relationship between the age of a car and the value of the car.

Negative trend graph

As the age of the car increases, the value of the car decreases. This is an example of a negative trend graph. There are some fluctuations in the values, but the overall trend is a negative one. The estimated trend line for this graph has a negative slope.

How to Calculate the Trend Line

How does someone calculate the trend line for a graph? A trend line indicates a linear relationship. The equation for a linear relationship is y = mx + b, where x is the independent variable, y is the dependent variable, m is the slope of the line, and b is the y-intercept. To find the slope of the equation of the trend line, m, use the formula: {eq}m = frac{Sigma(x - overline{ m x}) imes (y - overline{ m y})}{Sigma(x - overline{ m x})^2} {/eq} Then, find the y-intercept of the equation of the trend line, b, using the formula:

{eq}overline{ m y} = moverline{ m x} + b {/eq}

Here is an example of how to calculate the trend line.

This table shows the high temperatures in the fictional city of Park Falls for a one-week period.

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Day Temperature (F) 1 67 2 64 3 64 4 62 5 61 6 59 7 57 When calculating the line of best fit, the goal is to find the line for which the distance of each individual point from the line is the least. The formula is easiest to use in a step-by-step method, with the help of a table. To use the trend line formula, follow the steps: First, find the average of the x values, or {eq}overline{ m x} = frac{1 + 2 + . . .}{7} = 4 {/eq}, and the average of the y values, or {eq}overline{ m y} = frac{66 + 64 + . . .}{7} = 62 {/eq}. Next, find the distance between each x value and the average of the x values, and the distance between each y value and the average of the y values. For this table, the average of x is shown as X, and the average of y is shown as Y. x - X y - Y 1-4=-3 67-62=5 2-4=-2 64-62=2 3-4=-1 64-62=2 4-4=0 62-62=0 5-4=1 61-62=-1 6-4=2 59-62=-3 7-4=3 57-62=-5 Then, fill in the next two columns of the chart, multiplying (x - X) by (y - Y), and multiplying (x - X) by itself. x - X y - Y (x - X)(y - Y) (x - X)(x - X) 4-1=3 67-62=5 3x5=15 3x3=9 4-2=2 64-62=2 2x2=4 2x2=4 4-3=3 64-62=2 3x2=6 3x3=9 4-4=0 62-62=0 0x0=0 0x0=0 4-5=-1 61-62=-1 -1x-1=1 -1x-1=1 4-6=-2 59-62=-3 -2x-3=6 -2x-2=4 4-7=-3 57-62=-5 -3x-5=15 -3x-3=9

Now, find the totals for columns three and four.

study.com - What is a Trend Line? - Video & Lesson Transcript - Study.com

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