# Australian Bureau of Statistics

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 Australian CensusAtSchool

CaSQ 17B - Scatter plots: Correlation and fitting a trend line

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 How to: Get a Random Sample from CensusAtSchool Go to the CensusAtSchool Random Sampler to download a sample. Reference year: (select year) Sample size: At least 30 students Select questions: Year level, Concentration Game Location: Select Location Year level: All To project privacy there is a rule built into the sampler that the requested sample size cannot exceed 10% of the respondents for the parameters entered.

This task is designed to be completed by hand drawing a scatterplot. It can also be completed using Excel or a CAS calculator.

1. Using your CensusAtSchool random sample, enter both sets of thirty numbers as:
• a table in your workbook, or
• two columns in Excel, or
• two separate lists in your CAS calculator.

2. Create a scatter plot with your data.
• Think about which set of data is the independent and dependent variable
• Plan your axes to include the highest and lowest values in the data
• Include a title that includes the variable names.

3. Look at your graph. Can you see any trend or pattern to the data? Complete this sentence:

As school year level __________________, concentration time __________________.

4. Examine your scatter plot and circle the appropriate description:
 Direction Form Strength Positive Negative Linear Non-linear Strong Moderate Weak

5. Fit a trend line (sometimes called the line of best fit) to the data and complete the following sentence:
Each time the year level increases by 1 (year), the concentration time _________________ by ____ (seconds).

6. Estimate the value of the correlation coefficient (r) and explain what this indicates about the strength of the relationship.

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Extension:

7. Use the Random Sampler to choose your own data to create a scatterplot.

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8. Use linear regression to calculate the trend line and the correlation coefficient.

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9. Explain what this correlation coefficient indicates about the strength of the relationship.

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