A modeller compares two fitted models using residuals, defined as observed value minus predicted value. In increasing order of the explanatory variable, the residuals are
Linear model: −2.1,−0.4,1.2,1.5,0.2,−1.9-2.1,-0.4,1.2,1.5,0.2,-1.9−2.1,−0.4,1.2,1.5,0.2,−1.9
Quadratic model: −0.5,0.3,−0.2,0.4,−0.1,0.1-0.5,0.3,-0.2,0.4,-0.1,0.1−0.5,0.3,−0.2,0.4,−0.1,0.1.
Compare the residuals for the two models.
State which model is more appropriate, giving a reason.
Explain why the chosen model should still be used cautiously for extrapolation.
355 exam-style questions on OCR (MEI) A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 Process and language of hypothesis testing, 2.5.2 When to apply 1-tail and 2-tail tests, 2.5.3 Significance level and incorrect rejection, 2.5.4 Null and alternative hypotheses (binomial), 2.5.5 Conduct a binomial hypothesis test, 2.5.6 Critical and acceptance regions (binomial), 2.5.7 Distribution of the sample mean (A-level only), 2.5.8 Hypothesis test for a single mean (A-level only), 2.5.9 Critical and acceptance regions (mean) (A-level only), 2.5.10 Correlation as closeness to a straight line (A-level only), 2.5.11 Inference using a correlation coefficient (A-level only), and 2.5 Statistical Hypothesis Testing. Each one has a worked solution and a mark scheme showing where the marks go.