 # Informally Fitting a Line

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Examples, solutions, and videos to help Grade 8 students learn how to informally fit a straight line to data displayed in a scatter plot and make predictions based on the graph of a line that has been fit to data.

### New York State Common Core Math Grade 8, Module 6, Lesson 8

Lesson 8 Student Outcomes

• Students informally fit a straight line to data displayed in a scatter plot.
• Students make predictions based on the graph of a line that has been fit to data.

Lesson 8 Summary

• When constructing a scatter plot, the variable that you want to predict (i.e., the dependent or response variable) goes on the vertical axis. The independent variable (i.e., the variable not changed by other variables) goes on the horizontal axis.
• When the pattern in a scatter plot is approximately linear, a line can be used to describe the linear relationship.
• A line that describes the relationship between a dependent variable and an independent variable can be used to make predictions of the value of the dependent variable given a value of the independent variable.
• When informally fitting a line, you want to find a line for which the points in the scatter plot tend to be close to the line.

Lesson 8 Classwork

Example 1: Housing Costs
Let's look at some data from one midwestern city that indicates the sizes and sale prices of various houses sold in this city.
A scatter plot of the data is given below.

Exercises 1–6
1. What can you tell about the price of large homes compared to the price of small homes from the table?

2. Use the scatter plot to answer the following questions.
a. Does the plot seem to support the statement that larger houses tend to cost more? Explain your thinking.
b. What is the cost of the most expensive house, and where is that point on the scatter plot?
c. Some people might consider a given amount of money and then predict what size house they could buy. Others might consider what size house they want and then predict how much it would cost. How would you use the above scatter plot?
d. Estimate the cost of a 3,000 square foot house.
e. Do you think a line would provide a reasonable way to describe how price and size are related? How could you use a line to predict the price of house if you are given its size?

3. Draw a line in the plot that you think would fit the trend in the data.

a. What is your prediction of the price of a 3,000 square foot house?
b. What is the prediction of the price of a 1,500 square foot house?

5. Consider the following general strategies used by students for drawing a line. Do you think they represent a good strategy in drawing a line that will fit the data? Explain why or why not, or draw a line for the scatter plot using the strategy that would indicate why it is or why it is not a good strategy.
a. Laure thought she might draw her line using the very first point (farthest to the left) and the very last point (farthest to the right) in the scatter plot.
b. Phil wants to be sure that he has the same number of points above and below the line.
c. Sandie thought she might try to get a line that had the most points right on it.
d. Maree decided to get her line as close to as many of the points as possible.
6. Based on the strategies discussed in Exercise 5, would you change how you draw a line through the points? Explain your answer.

Example 2: Deep Water
Does the current in the water go faster or slower when the water is shallow? The data on the depth and speed of the Columbia River at various locations in Washington state listed below can help you think about the answer.
a. What can you tell about the relationship between the depth and velocity by looking at the numbers in the table?
b. If you were to make a scatter plot of the data, which variable would you put on the horizontal axis and why?

Exercises 7–9
7. A scatter plot of the Columbia River data is shown below.
a. Choose one point in the scatter plot and describe what it means in terms of the context.
b. Based on the scatter plot, describe the relationship between velocity and depth.
c. How would you explain the relationship between the velocity and depth of the water?
d. If the river is two feet deep at a certain spot, how fast do you think the current would be? Explain your reasoning.

8. Consider the following questions:
a. If you draw a line to represent the trend in the plot, will it make it easier to predict the velocity of the water if you know the depth? Why or why not?
b. Draw a line that you think does a reasonable job of modeling the trend on the scatter plot above. Use the line to predict the velocity when the water is 8 feet deep.

9. Use the line to predict the velocity for a depth of 8.6 feet. How far off was your prediction from the actual observed velocity for the location that had a depth of 8.6 feet? Lesson 8 Exit Ticket

The plot below is a scatter plot of mean temperature in July and mean inches of rain per year for a sample of midwestern cities. A line is drawn to fit the data.

1. Choose a point in the scatter plot and explain what it represents.

2. Use the line provided to predict the mean number of inches of rain per year for a city that has a mean temperature of 70 in July.

3. Do you think the line provided is a good one for this scatter plot? Explain your answer.

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