The ambient temperature, T ∘CT\,^\circ\text{C}T∘C, and the cooling time, CCC minutes, required for a specialized industrial freezer to freeze a specific chemical sample were recorded on 6 different operating days. The data is summarized in the table below.
| Day | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| TTT | 20 | 22 | 25 | 28 | 30 | 31 |
| CCC | 14 | 16 | 21 | 26 | 32 | 35 |
∑T=156,∑C=144,∑T2=4154,∑C2=3818,∑TC=3930\sum T = 156, \quad \sum C = 144, \quad \sum T^2 = 4154, \quad \sum C^2 = 3818, \quad \sum TC = 3930∑T=156,∑C=144,∑T2=4154,∑C2=3818,∑TC=3930
Calculate the values of SCCS_{CC}SCC, STCS_{TC}STC and STTS_{TT}STT for these data.
Calculate the product moment correlation coefficient (PMCC) for these data.
Interpret your value of the PMCC in the context of the relationship between ambient temperature and cooling time.
On a suitable grid, draw a scatter diagram of cooling time against ambient temperature for these 6 days.
Determine the equation of the regression line of CCC on TTT in the form C=a+bTC = a + bTC=a+bT.
Use your regression line to estimate the cooling time required when the ambient temperature is 27 ∘C27\,^\circ\text{C}27∘C.
Practise Edexcel A Level Maths Regression, Correlation and Hypothesis Testing with exam-style questions for A Level Maths. 100 questions covering Exponential Models, Measuring Correlation, and Hypothesis Testing for Zero Correlation, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.