Topic 4.4: Cumulative Frequency and Box Plots Questions

State the range of possible values of the Pearson correlation coefficient r.

For data with x ranging from 10 to 50, state whether using the regression line to predict y at x = 30 is interpolation or extrapolation.

A GDC gives r = 0.97 for the relationship between two quantities. State whether a line of best fit would be a good model, and why.

Describe how to find the equation of the regression line of y on x from bivariate data on a GDC.

Two variables have r = 0.15. Describe the correlation.

A scatter diagram shows points rising from lower-left to upper-right in a tight band. Describe the correlation.

State what a Pearson correlation coefficient of r = −0.88 tells you about two variables.

A regression line is y = 1.14x + 0.58. Use it to estimate y when x = 6.

A researcher studies how the temperature x (in °C) affects the number of cold drinks y sold at a kiosk. The recorded data, for temperatures from 18 °C to 32 °C, gives the regression line of y on x as y = 8.5x − 96 (from a GDC), with r = 0.96.

Explain why predictions from a regression line are more trustworthy when r is close to ±1.

A regression line of height (y cm) on age (x years) is y = 5.2x + 80. Interpret the y-intercept 80 in context.

For data with x from 10 to 50, classify a prediction at x = 70 and comment on its reliability.

A regression line of y on x is y = −2.5x + 40. Interpret the gradient in context (x = price in $, y = units sold).

A coach records the number of training hours per week (x) and the distance jumped (y, in metres) for 8 athletes. Entering the data into a GDC gives the Pearson correlation coefficient r = 0.92.

A study finds a strong positive correlation between ice-cream sales and drowning incidents. Explain why ice-cream sales do not cause drownings.

A lifeguard records the daily maximum temperature x (°C) and the number of visitors y at an outdoor pool on 8 days.

x: 12, 15, 18, 21, 24, 27, 30, 33

y: 55, 82, 90, 120, 150, 175, 210, 240

(a) Use your GDC to find the Pearson correlation coefficient r.

(b) Describe the correlation between temperature and number of visitors.

A shop owner records the weekly advertising spend x (in hundreds of dollars) and the number of items sold y over 7 weeks.

x: 2, 4, 5, 7, 8, 10, 12

y: 34, 48, 52, 70, 78, 95, 110

(a) Use your GDC to find the equation of the regression line of y on x.

(b) Use your equation to estimate the number of items sold in a week when the advertising spend is $600.

Order these correlation coefficients from weakest to strongest linear relationship: r = 0.45, r = −0.91, r = 0.10, r = −0.6.

An app's monthly subscriber count y (in thousands) is recorded over its first 6 months, where x is the month number.

x: 1, 2, 3, 4, 5, 6

y: 5, 9, 12, 16, 21, 24

(a) Find the equation of the regression line of y on x.

(b) Use the equation to estimate the number of subscribers in month 12.

(c) State, with a reason, whether this estimate is likely to be reliable.

Six data points are (1, 3), (2, 5), (3, 6), (4, 8), (5, 9), (6, 11). A seventh point (7, 1) is then added.

(a) Find the correlation coefficient r for the original six points.

(b) Find r for all seven points.

(c) Explain what the change in r shows about the seventh point.