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Scatter Plots and Line of Best Fit Date: ____________
REVIEW: Shapes of a Curve
Linear ( + ) Linear ( - ) Quadratic (+) Quadratic ( - )** *To be used at a later date!
Scatter Plots
To analyze two sets of data, you can create a scatter plot.
EXAMPLE: Is there a relationship between height and shoe size?
Trend Line/Line of Best Fit
- A trend line models the data in the scatter plot by showing the general direction of the data.
o Fits the data as closely as possible, but may not pass through any of the data points o Approximates a balance of points above and below the line
Height (inches) Shoe Size Height (inches) Shoe Size
EXAMPLE: The trend line (line of best fit) is shown for the data on the graph.
- Write the equation of the trend line.
- Approximate the number of electric hybrid cars sold in 2010.
Linear Regression
- Linear regression is the method used to calculate the line of best fit. o Using a calculator is the most precise way to do a linear regression
Types of Linear Regression (Lines of Best Fit)
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The correlation coefficient (๐๐) is a number between -1 and 1 that indicates the direction and strength of the linear relationship between a set of data that uses two variables
- When ๐๐ is close to 1 , there is a strong positive correlation
- When ๐๐ is close to -1 , there is a strong negative correlation
- When ๐๐ is close to 0 , there is a weak correlation.
๐๐ is the slope
๐๐ is the y-intercept
2. Using the data provided: a. Find the equation of the model b. Graph the equation โ is the function is a good model (look at ๐๐)? c. Answer the question.
a.
b.
c. Predict what your y-value might be if x = 30.
3. Temperatures at different times of the day are shown. Enter the data points in Desmos as a list of ordered pairs.
a. How can you describe the relationship between temperature and time?
b. Would a linear model be a good fit for the data? Explain.
