# Data handling: Use variance and regression analysis to interpolate and extrapolate bivariate data

### Subject outcome

Subject outcome 4.2: Use variance and regression analysis to interpolate and extrapolate bivariate data

### Learning outcomes

• Calculate:
• variance, and
• standard deviation manually for small sets of data only.
• Interpret the meaning of variance and standard deviation for small sets of data only.
• Represent bivariate numerical data as a scatter plot.
• Identify intuitively whether a linear, quadratic or exponential function would best fit the data.
• Draw the intuitive line of best fit.
Range:

• Data given should include problems related to health, social, economic, cultural, political and environmental issues.
• For small sets of data only (limited to 8).
• Use least squares regression method to determine a function which best fits a given set of bivariate data.
• Use the regression line to predict the outcome of a given problem.

### Unit 1 outcomes

By the end of this unit you will be able to:

• Calculate variance for ungrouped data manually.
• Calculate standard deviation for ungrouped data manually.
• Interpret variance and standard deviation.

### Unit 2 outcomes

By the end of this unit you will be able to:

• Draw a scatter plot.
• Understand when it is appropriate to use a scatter plot.
• Draw an intuitive line of best fit.

### Unit 3 outcomes

By the end of this unit you will be able to:

• Determine the linear regression equation $\scriptsize \hat{y}=a+bx$.
• Use the regression line to predict the outcome of a given problem.