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NSWMaths Standard 2Quick questions
Year 12: Statistical Analysis
Quick questions on The least-squares regression line for HSC Maths Standard 2
11short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.
What is the least-squares regression line?Show answer
For bivariate data, the least-squares regression line is the straight line that minimises the sum of the squared vertical distances from the data points to the line. It is the standard "best-fit" line for linear association.
What is finding the line on a calculator?Show answer
You will not be asked to compute the gradient and intercept by hand. The procedure on a NESA-approved scientific calculator:
What is predicting from ?Show answer
Substitute the value into the line equation. This is the model's predicted at that . The actual value may be slightly different; the line is the best linear fit, not a guarantee.
What is interpreting the gradient?Show answer
The gradient has units of (y units) per (x unit). For every unit increase in , changes by units on average.
What is interpreting the -intercept?Show answer
The intercept is the predicted value when . In context this is sometimes meaningful (e.g. base salary at zero years of experience) and sometimes extrapolation (e.g. predicted food spending at zero income).
What is when to use the line?Show answer
The least-squares line is appropriate when:
What is interpreting the intercept?Show answer
Intercept \38000\. This is meaningful if the dataset includes new cars; otherwise the intercept is extrapolation.
What is australian context (ABS-style)?Show answer
A regression of weekly entertainment spending on household income for ABS-style data gives:
What is wrong units?Show answer
The gradient has units of (y units) per (x unit). Include them explicitly.
What is interpreting the intercept without checking for extrapolation?Show answer
If the data does not include near zero, the intercept is an extrapolation. Mention this.
What is confusing the regression line with the line connecting two points?Show answer
The least-squares line is the best fit over the entire dataset. Do not draw a line through any two specific points.