Question

construct and interpret scatter plots
below is a table that has the number of houses in a neighborhood and the number of trees in that same neighborhood. create a scatter plot using the data provided and answer the following questions.

houses	trees
120	300
60	400
380	38
100	450
20	570
220	245
340	150
150	360

the relationship between \temperature and cones sold is: positive or negative
linear or nonlinear
strong or weak
use a trend line to predict the number of trees in a neighborhood if there are 160 houses.
are there any outliers? if so, list which point(s) they are.
which ordered pair would best fit the trend of the scatter plot? (120, 180) (300, 210) (20, 510)
using a trend line, predict how many trees would be in the neighborhood if there were 300 houses.
based on the trend, if there were 180 trees, would you expect there to be more or less than 200 houses? why?

Explanation:

Step1: Identify the data points

The data points are pairs of (Houses, Trees) from the table: (280,450), (120,300), (60,400), (380,38), (100,450), (20,570), (220,245), (340,150), (150,360)

Step2: Analyze the relationship type

By observing the scatter - plot (not actually drawn here but conceptually), as the number of houses increases, the number of trees does not follow a clear upward or downward linear trend. The relationship is non - linear and weak. There is no consistent pattern of increase or decrease.

Step3: Identify outliers

The point (380,38) seems to be an outlier as it is far from the general cluster of points.

Step4: Predict using a trend - line (approximate conceptually)

To predict the number of trees for 300 houses and 160 houses, we would draw a trend - line (if we had a proper plot). But conceptually, we can't precisely calculate without a regression analysis. However, we can say that for 300 houses, looking at the data distribution, it might be around 200 - 250 trees (a very rough estimate). For 160 houses, it could be around 300 - 350 trees (again a rough estimate).

Step5: Choose the best - fit ordered pair

Among (120,180), (300,210), (20,510), (300,210) seems to be the most reasonable as it is in the general range of what we might expect based on the data distribution for a value of 300 houses.

Step6: Answer the last question

If there were 180 trees, based on the general trend of the data (weak and non - linear), we would expect less than 200 houses. Because most of the points with lower tree counts are associated with lower house counts.

Answer:

• Relationship: Non - linear, Weak
• Outlier: (380,38)
• Prediction for 300 houses: Roughly 200 - 250 trees
• Prediction for 160 houses: Roughly 300 - 350 trees
• Best - fit ordered pair: (300,210)
• If 180 trees, expect less than 200 houses.