Topic 2.6: Regression and Interpolation Questions

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 = 3.2x + 5. Interpret the gradient in context where x is hours worked and y is items produced.

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

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.

Define interpolation in the context of using a regression line.

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

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.

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. (a) Is this interpolation or extrapolation? (b) Give one reason why this prediction may not be reliable.

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 regression line of weight (kg) on age (months) is W = 0.5a + 4, fitted from ages 2 to 24 months. Estimate the weight at 12 months.

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

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

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.

A model predicts a value of −15 for the number of items sold. State what this tells you about the model at that input.

Define extrapolation in the context of using a regression line.

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

A GDC linear regression for two variables p and q returns a = 0.247 and b = 11.83 (TI form: y = ax + b). Write the regression equation for q in terms of p, with each coefficient to 3 s.f.

Explain why extrapolation can give unreliable predictions.

The regression line of temperature drop y on time x is y = 1.5x + 2. Interpret the y-intercept.