2.2 Data Presentation and Interpretation

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Question 8

The variables $x\,$ and $y\,$ are recorded for a set of 15 observations. Two different codings are used.

Coding A: $p = \log_{10} x$ and $q = \log_{10} y$ . The product moment correlation coefficient between $p\,$ and $q\,$ is 0.921, and the regression line of $q\,$ on $p\,$ is $q = 0.664 + 1.48 p$ .

Coding B: $u = x$ and $v = \log_{10} y$ . The product moment correlation coefficient between $u\,$ and $v\,$ is 0.998, and the regression line of $v\,$ on $u\,$ is $v = 0.802 + 0.0913 u$ .

State, giving a reason, which of the models $y = ax^{b}$ and $y = kc^{x}$ is better supported by these data.

[2]

Using the better-supported model, find the values of its two constants. Give your answers to 3 significant figures.

[4]

Explain why the value 1.48 in Coding A's regression line cannot be interpreted as the increase in $y\,$ produced by an increase of 1 in $x$ .

[2]

2.2 Data Presentation and Interpretation

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Question 8

The variables $x\,$ and $y\,$ are recorded for a set of 15 observations. Two different codings are used.

Coding A: $p = \log_{10} x$ and $q = \log_{10} y$ . The product moment correlation coefficient between $p\,$ and $q\,$ is 0.921, and the regression line of $q\,$ on $p\,$ is $q = 0.664 + 1.48 p$ .

Coding B: $u = x$ and $v = \log_{10} y$ . The product moment correlation coefficient between $u\,$ and $v\,$ is 0.998, and the regression line of $v\,$ on $u\,$ is $v = 0.802 + 0.0913 u$ .

State, giving a reason, which of the models $y = ax^{b}$ and $y = kc^{x}$ is better supported by these data.

[2]

Using the better-supported model, find the values of its two constants. Give your answers to 3 significant figures.

[4]

Explain why the value 1.48 in Coding A's regression line cannot be interpreted as the increase in $y\,$ produced by an increase of 1 in $x$ .

[2]

2.2 Data Presentation and Interpretation

Question 8

Markscheme

2.2 Data Presentation and Interpretation

Question 8

Markscheme

2.2 Data Presentation and Interpretation

Question 8

2.2 Data Presentation and Interpretation Questions

2.2 Data Presentation and Interpretation

Question 8

2.2 Data Presentation and Interpretation Questions