Topic 2.6: Regression and Interpolation Questions

A GDC gives the regression line y = −3.4x + 52. What happens to y as x increases?

Data is collected for x between 10 and 50. State whether a prediction at x = 35 is interpolation or extrapolation.

A researcher fits both a linear and an exponential regression to a dataset. The linear model gives R² = 0.74. The exponential model gives R² = 0.97.

Harbour depth is measured hourly for two days. The readings rise to a peak, fall to a low, and repeat this pattern about every 12 hours. Which model fits best?

A student uses a quadratic model to predict the temperature at an Antarctic research station. The model was built using data for months 1 to 12. The student uses the model to predict the temperature in month 18.

Data covers x from 10 to 50. Classify a prediction at x = 65.

Describe how to find the equation of the regression line of y on x using a GDC.

The regression line of y on x is y = 3.2x + 5. Interpret the gradient in context where x is hours worked and y is items produced.

The depth of water in a harbour is measured every hour for two days. A scatter plot shows the depth rising to a maximum, falling to a minimum, then rising again to a second maximum, repeating roughly every 12 hours. State, with a reason, which type of model is most appropriate.

A regression model is built using data for ages 5 to 18 years. State whether each of the following predictions is interpolation or extrapolation.

The regression line of y on x is y = 0.8x + 12. Use it to predict y when x = 25.

Explain why extrapolation can give unreliable predictions.

A study of fuel consumption F (L/100km) versus engine size e (litres) uses data from e = 1.0 to 4.0 L. Regression: F = 3.4e + 2.1. Predict the fuel consumption of a car with a 2.5 L engine, and comment on the reliability.

A regression model is fit to a child's weight W (kg) over ages 5 to 15. State a reasonable domain over which to apply the model, and justify.

Data is collected monthly for one year showing electricity use. A scatter plot shows a wave-like pattern repeating every 12 months.

A regression line is only valid for x between 5 and 40. State the largest and smallest x-values for which a prediction would count as interpolation.

State whether predictions are generally more reliable for interpolation or extrapolation.

A regression line of revenue R ($) on units sold u is R = 8u − 200, fitted for u from 50 to 400. Estimate the revenue when 250 units are sold.

A GDC gives r = −0.97 for a set of bivariate data. Describe the correlation.

For a set of bivariate data a calculator gives r = −0.94. Describe the correlation.