2-5 Using Linear Models Make predictions by writing linear equations that model real-world data.

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Presentation transcript:

2-5 Using Linear Models Make predictions by writing linear equations that model real-world data.

Scatter Plots A scatter plot is a graph that displays two sets of data as ordered pairs. Scatter plots can help show whether or not two sets of data are related.

Making a Scatter Plot Make a scatter plot for the data What’s a car worth? Age (yr) Value (dollars) 3 11,000 1 15,000 2 12,000 4 8,000 7 3,000 5 7,000 8 1,000 6,000 10,000 6

Correlation A correlation is a relationship between the sets of data Also called a trend Positive correlation or trend

Correlation Negative correlation or trend

Correlation No correlation or trend

Line of Best Fit A line you draw on a graph to approximate the relationship between data sets. Also called a trend line A line of best fit should have an equal number of data points on each side If there is no correlation, you cannot draw a line of best fit

You Try! Create a scatter plot for the data and draw the trend line. 2 5 4 3 3.5 7 4.5 9 6

Making Predictions What is the approximate weight of a 7 month old panda? We have just used interpolation to estimate a value between two known values using a line of best fit. Extrapolation is used to predict a value outside the range of known values. Ex: Use your model to find the body weight of a 3-year old panda.

Causation A change in one quantity causes a change in the second quantity. Correlation does not always imply causation

Using a Calculator Correlation coefficient (r) can be found using a graphing calculator. Ranges between -1 and 1 The nearer r is to 1 or -1, the more closely the trend line fits the data r close to 1 shows a strong positive correlation r close to -1 shows a strong negative correlation r close to 0 means a weaker correlation or no correlation

Using a Calculator Press STAT and then 1 to select EDIT Enter x-values into L1 and y-values into L2 (if x-values are years, do not enter the year, but enter 1 for one year from the start, 2 for 2 years from start, etc.) Press STAT then move Right to the CALC menu Move Down to LinReg(ax+b) and press Enter Press Enter again a will represent slope b will represent the y-intercept And r will show the correlation coefficient (NOT r2)

Assignment ODDS P.96 #7-17