Question

Based on the line of best fit in the scatterplot above, which of the following is the closest to the average annual increase in coyotes in Yellowstone Park between 1995 and 2000 ? A) 22 B) 24 C) 26 D) 28

Short answer

Based on the line of best fit in the scatterplot, the closest to the average annual increase in coyotes in Yellowstone Park between 1995 and 2000 is found by first identifying the coordinates for these years on the line, calculating the difference in the number of coyotes (D) and the number of years (Y), and then dividing D by Y. Finally, compare the result to the given options (A: 22, B: 24, C: 26, and D: 28) and select the closest option as the correct answer.

Step-by-step solution

Identify the Coordinates for 1995 and 2000

To find the increase between 1995 and 2000 based on the line of best fit, let's first find the coordinates on the line of best fit for each year. (You can usually do this by looking at the scatterplot and finding the points where the line crosses the vertical lines representing 1995 and 2000 on the x-axis.) Write down the coordinates as (Year, Number of Coyotes).

Calculate the Difference in the Number of Coyotes

Calculate the difference in the number of coyotes between 1995 and 2000. You can do this by subtracting the y-coordinate (number of coyotes) at 1995 from the y-coordinate at 2000. Let's call this difference D.

Calculate the Number of Years Between 1995 and 2000

Calculate the number of years between 1995 and 2000. This is equal to the difference in the x-coordinates (years) of the points for 1995 and 2000. Let's call this Y.

Calculate the Average Annual Increase

Now, to find the average annual increase, divide the difference in the number of coyotes (D) by the number of years (Y). This will give you the average increase in the number of coyotes per year.

Compare the Result to the Given Options

Compare the result of the average annual increase to the given options (22, 24, 26, and 28). Choose the option that is closest to the calculated average annual increase.

Choose the Correct Answer

Based on the comparison, select the option that is closest to the average annual increase in the number of coyotes in Yellowstone Park between 1995 and 2000. This is your answer.

Key concepts

Scatterplot Interpretation

Understanding scatterplots is crucial in data analysis. A scatterplot is a type of graph that uses Cartesian coordinates to display values for typically two variables for a set of data. In our case, each point on the scatterplot represents a year and the corresponding number of coyotes in that year.

• The x-axis represents the year, ranging from 1995 to 2000.
• The y-axis represents the number of coyotes in Yellowstone Park.

Interpreting a scatterplot involves looking for patterns, such as trends over time. This can help identify correlations between the variables: years and the number of coyotes. A scatterplot shows how these data points are distributed across the graph.
Notably in a scatterplot, the line of best fit might also be plotted to indicate a general trend, simplifying the pattern recognition. Seeing where this line crosses the vertical lines for specific years helps determine the coordinates of interest.

Average Annual Increase

To assess "average annual increase," you must first identify the total change and then distribute it over the entire time period.
Suppose the number of coyotes grew from a certain number in 1995 to a higher number in 2000 as per the scatterplot's line of best fit. Here’s how to calculate:

• Identify Coordinates: For both 1995 and 2000, identify how many coyotes were recorded.
• Find Total Increase: Subtract the 1995 count from the 2000 count.
• Calculate Years Between: There are 5 years between 1995 and 2000.

Finally, to determine average annual increase, divide the total increase by the number of years: \[ \text{Average Annual Increase} = \frac{\text{Total Increase}}{5} \] This value is then compared against provided options to find the closest match.

Line of Best Fit

The line of best fit is a crucial element of linear regression analysis. It summarizes the relationship between the variables across all data points plotted on a scatterplot.
This line minimizes the distance between itself and all the data points on the graph, hence its alternate name, "least squares regression line."
To understand this line, consider the following:

• Slope: The slope indicates the average change in the number of coyotes per year. A positive slope, which is common in growth scenarios, shows an increase.
• Intersection Points: Selecting the points of intersection with the years in question, like 1995 and 2000, allows us to extract useful coordinates.

When dealing with a scatterplot, the line of best fit helps to estimate values for unobserved sections or to predict future values based on historical data. In this instance, finding its coordinates for 1995 and 2000 enables calculation of average annual trends.