1.6 Exponentials and Logarithms

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Question 1

40%

A logistics manager is studying the relationship between the age of a delivery van, $x\,$ years, and its current resale value, $y\,$ thousands of pounds.

She records the data for 10 vans and calculates the product moment correlation coefficient between the age and the resale value to be -0.51.

Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between the age of a van and its resale value.

[3]

The manager decides to test a non-linear model. She codes the data using $m = \log_{10}x$ and $n = \log_{10}y$ and finds the regression line to be $n = 1.35 - 0.48 m$ .

The product moment correlation coefficient between $m\,$ and $n\,$ is calculated as -0.94.

Explain how this value supports the use of a non-linear model.

[1]

Show that the relationship between $x\,$ and $y\,$ can be expressed in the form $y = ax^b$ , where $a\,$ and $b\,$ are constants to be determined.

[5]

1.6 Exponentials and Logarithms

Question 1

40%

A logistics manager is studying the relationship between the age of a delivery van, $x\,$ years, and its current resale value, $y\,$ thousands of pounds.

She records the data for 10 vans and calculates the product moment correlation coefficient between the age and the resale value to be -0.51.

Stating your hypotheses clearly and using a 5% level of significance, test whether or not there is evidence of a negative correlation between the age of a van and its resale value.

[3]

The manager decides to test a non-linear model. She codes the data using $m = \log_{10}x$ and $n = \log_{10}y$ and finds the regression line to be $n = 1.35 - 0.48 m$ .

The product moment correlation coefficient between $m\,$ and $n\,$ is calculated as -0.94.

Explain how this value supports the use of a non-linear model.

[1]

Show that the relationship between $x\,$ and $y\,$ can be expressed in the form $y = ax^b$ , where $a\,$ and $b\,$ are constants to be determined.

[5]

1.6 Exponentials and Logarithms

Question 1

Markscheme

1.6 Exponentials and Logarithms

Question 1

Markscheme

1.6 Exponentials and Logarithms

Question 1

1.6 Exponentials and Logarithms Questions

1.6 Exponentials and Logarithms

Question 1

1.6 Exponentials and Logarithms Questions