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What do you notice? What do you wonder?
A scatterplot. Horizontal, from 60 to 80, by 5's, labeled number of people, thousands. Vertical, 105 to 140, by 5’s, labeled maximum noise level, decibels. 12 dots, straight line trending upward and to the right.
Watch the video, and record the weight for the number of oranges in the box.
| number of oranges | weight in kilograms |
|---|---|
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 |
Create a scatter plot of the data.
The scatter plot shows the sale price of several food items, , and the cost of the ingredients used to produce those items, , as well as a line that models the data. The line is also represented by the equation .
A scatterplot. Horizontal from 0 to 4 by 0 point 5s, labeled ingredient cost, dollars. Vertical, 0 to 12, by 0 point 5's, labeled sale price, dollars. 24 dots trending upward and to the right. Line of best fit trends upwards and to the right, passing through 0 point 41 comma 2 point 19.
A. A scatterplot. Horizontal from 0 to 24 by 2's, labeled age, years. Vertical, 0 to 350, by 25's, labeled reaction time, milliseconds. 21 dots trending linearly downward and right. Dot 1 at approximately 10 comma 310, Dot 21 at approximately 22 comma 185, with line of best fit.
B. A scatterplot. Horizontal from 0 to 7 by 1's, labeled number of bananas. Vertical, 0 to 3 point 5, by 0 point 5's, labeled price in dollars. 14 dots trending linearly upward and right. Dot 1 at 1 comma 0 point 5, Dot 14 at 6 comma 2 point 53, with line of best fit.
C. A scatterplot. Horizontal from 0 to 500 by 50's, labeled room size, square feet. Vertical, 0 to 2,200, by 100's, labeled cost to install flooring, dollars. 14 dots trending linearly upward and right. Dot 1 at approximately 150 comma 700, Dot 14 at approximately 450 comma 1,800, with line of best fit.
D. A scatterplot. Horizontal from 0 to 5 point 5 by 0 point 5's, labeled temperature, degrees Celsius. Vertical, 0 to 24, by 2's, labeled volume, cubic centimeters. 18 dots trending linearly downward and right. Dot 1 at approximately 1 point 5 comma 22, Dot 18 at approximately 4 point 5 comma 15, with line of best fit.
While working in math class, it can be easy to forget that reality is somewhat messy. Not all oranges weigh exactly the same amount, beans have different lengths, and even the same person running a race multiple times will probably have different finishing times. We can approximate these messy situations with more precise mathematical tools to better understand what is happening. We can also predict or estimate additional results as long as we continue to keep in mind that reality will vary a little bit from what our mathematical model predicts.
For example, the data in this scatter plot represents the price of a package of broccoli and its weight. The data can be modeled by a line given by the equation . The data does not all fall on the line because there may be factors other than weight that go into the price, such as the quality of the broccoli, the region where the package is sold, and any discounts happening in the store.
A scatterplot. Horizontal, from 0 to 3, by 0 point 5's, labeled weight in pounds. Vertical, 0 to 2 point 5, by 0 point 25s, labeled price in dollars.
12 dots trending upward and to the right. A line of best fit passes through the y axis at 0 comma 0 point 92, and trends upwards and to the right, passing through three dots.
We can interpret the -intercept of the line as the price for the package without any broccoli (which might include the cost of things like preparing the package and shipping costs for getting the vegetable to the store). In many situations, the data may not follow the same linear model farther away from the given data, especially as one variable gets close to zero. For this reason, the interpretation of the -intercept should always be considered in context to determine if it is reasonable to make sense of the value in that way.
We can interpret the slope as the approximate increase in price of the package for the addition of 1 pound of broccoli to the package.
The equation also allows us to predict prices of packages of broccoli that have weights near the weights observed in the data set. For example, even though the data does not include the price of a package that contains 1.7 pounds of broccoli, we can predict the price to be about $1.70 based on the equation of the line, since .
On the other hand, it does not make sense to predict the price of 1,000 pounds of broccoli with this data because there may be many more factors that influence the pricing of packages that far away from the data presented here.