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.

0 1 2 3 4 5 6 7 8 90

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Age (yr)

Valu

e (d

olla

rs)

Making a Scatter Plot• Make a scatter plot for the data• What’s a car worth?

Age (yr)

Value (dollars)

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 3 6,000

2 10,000 6 6,000

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 2

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3 3.5

7 4.5

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6 4 1 2 3 4 5 6 7 8 9 100

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1 2 3 4 5 6 7 8 9 100

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Making Predictions

• What is the approximate weight of a7 month old panda?

• We have just used interpolation toestimate 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