Regression, Correlation and Hypothesis Testing

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The temperature of water ( $w∘Cw^\circ\text{C}$ ) in a kettle $t\,$ minutes after it was boiled is recorded in the table below


$t$	1	3	6	9	11	15	20
$w$	92	76	65	50	46	33	25

The data is coded using the changes of variable $x = t$ and $y = \log_{10} w$

The regression line of $x\,$ on $y\,$ is found to be $y = 1.99 - 0.031 x$

Given that the data can be modelled by an equation in the form $w = ab^t$ where $a\,$ and $b\,$ are constants. Find the values of $a\,$ and $b\,$ to 3 significant figures.

[3]

Give an interpretation of the constant $a\,$ in this equation.

[1]

Explain why this model is not reliable for calculating the temperature after 1 hour.

[1]

Regression, Correlation and Hypothesis Testing Questions

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.