Fitting a linear model to numerical data
General Mathematics · Unit 3 — Bivariate data and time series analysis, sequences and Earth geometry · Bivariate data analysis 2
Learning objectives (6)
LO-1Construct a residual plot and use it to assess the appropriateness of fitting a linear model to the data.LO-2Distinguish between interpolation and extrapolation.LO-3Interpret the 𝑦-intercept and slope (gradient) of the fitted line.LO-4Model a linear relationship by using technology to fit a least-squares line to the data, in the form of 𝑦 = 𝑚𝑥 + 𝑐 where 𝑚 is slope (gradient) and 𝑐 is 𝑦-intercept.LO-5Understand and use 𝑚 = 𝑟 𝑠𝑦 𝑠𝑥 and 𝑐 = 𝑦 − 𝑚𝑥 to determine the equation of a least-squares line, where 𝑚 is slope (gradient), 𝑟 is correlation coefficient, 𝑠𝑦 is (sample) standard deviation of 𝑦 values, 𝑠𝑥 is (sample) standard deviation of 𝑥 values, 𝑐 is 𝑦-intercept, 𝑦 is mean of 𝑦 values and 𝑥 is mean of 𝑥 values.LO-6Use the equation of the least-squares line to make predictions.
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