Linear model for scatter plots

Task goals

• Substitute a given x-value into the equation of a line of best fit (y = mx + c) to predict the corresponding y-value.
• State the gradient and y-intercept of a line of best fit from its equation, or write the equation given the gradient and y-intercept.
• Find the gradient of a line of best fit from two points on it, and use a known y-intercept (or one of the points) to write its equation.
• Distinguish interpolation (predicting within the range of the original data) from extrapolation (predicting beyond it).
• Explain why an extrapolated prediction is generally less reliable than an interpolated one.
• Explain how the strength of a correlation (how closely points cluster around the line) and the sample size affect confidence in a prediction.
• Work backwards from a known y-value to find the corresponding x-value using the equation of the line of best fit.