The temperature of the water, $∘Cw\,^{\circ}\text{C}$ , in a kettle is recorded $t\,$ minutes after the kettle boiled.

$t$ : 1, 3, 6, 9, 11, 15, 20

$w$ : 92, 76, 65, 50, 46, 33, 25

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

The regression line of $y\,$ on $x\,$ is found to be

$y = 1.98 - 0.0298 x$

Given that the data can be modelled by an equation of the form $w = ab^{t}$ , where $a\,$ and $b\,$ are constants, find the value of $a\,$ and the value of $b$ . Give your answers to 3 significant figures.

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

Explain why this model is not reliable for predicting the temperature of the water one hour after the kettle boiled.

The temperature of the water, $∘Cw\,^{\circ}\text{C}$ , in a kettle is recorded $t\,$ minutes after the kettle boiled.

$t$ : 1, 3, 6, 9, 11, 15, 20

$w$ : 92, 76, 65, 50, 46, 33, 25

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

The regression line of $y\,$ on $x\,$ is found to be

$y = 1.98 - 0.0298 x$

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

Explain why this model is not reliable for predicting the temperature of the water one hour after the kettle boiled.

2 Statistics

Question 398

Markscheme

2 Statistics

Question 398

Markscheme

2 Statistics

Question 398

2 Statistics Questions

2 Statistics

Question 398

2 Statistics Questions