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6 exam-style questions with model answers, plus 8 quick multi-choice questions — every question on the site for this standard, grouped by the 2 pages of notes they come from.
Write a full answer before you reveal the model one — that comparison is where the marks come from. Every block links back to the notes that teach it.
For an investigation into whether a house's floor area is related to its sale price, identify the explanatory and response variables and justify the choice. State one requirement the response variable must meet.
A scatter plot of daily maximum temperature against ice cream sales for a NZ dairy shows a positive relationship with moderate scatter, and the points curve upward more steeply above about 24 °C. Describe the relationship and explain the shape in context.
A student investigating the relationship between a student's weekly hours of paid work and their end-of-year grade average notices the scatter plot contains two distinct clusters of points rather than one cloud. Discuss what this indicates and how she should proceed.
A model relating a runner's weekly training kilometres (x) to their half-marathon time in minutes (y) is y = 148 − 0.62x. Interpret the slope, and predict the time for someone training 50 km per week.
A student's residual plot for a linear model shows the residuals forming a clear curved arch — positive in the middle of the range and negative at both ends. Explain what this indicates and what she should do.
A student fits a linear model relating a town's annual rainfall (mm) to the region's annual pasture growth (kg dry matter per hectare) using 15 years of data covering rainfall from 620 mm to 1 150 mm. She uses it to predict pasture growth in a drought year with 380 mm of rainfall, and reports the figure without qualification. Evaluate this.