• Syllabus

3.7

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Sub sections and their related questions

Introduction to bivariate distributions.

• SPNone.1.hl.TZ0.10a: (i)     Calculate the correlation coefficient for this sample. (ii)     Calculate the...
• SPNone.1.hl.TZ0.10b: (i)     Calculate the equation of the least squares regression line of $w$ on $h$ . (ii)    ...
• 14M.1.hl.TZ0.11: The random variables $X$, $Y$ follow a bivariate normal distribution with product moment...
• 15M.1.hl.TZ0.5a: Calculate the product moment correlation coefficient.

Covariance and (population) product moment correlation coefficient $\rho$.

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Proof that $\rho = 0$ in the case of independence and $\pm 1$ in the case of a linear relationship between $X$ and $Y$.

None

Definition of the (sample) product moment correlation coefficient R in terms of n paired observations on X and Y. Its application to the estimation of ρ.

• 15M.1.hl.TZ0.5a: Calculate the product moment correlation coefficient.

Informal interpretation of $r$, the observed value of $R$. Scatter diagrams.

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The following topics are based on the assumption of bivariate normality.

• 15M.1.hl.TZ0.5b: Find the $p$-value.

Use of the $t$-statistic to test the null hypothesis $\rho = 0$ .

• 15M.1.hl.TZ0.5b: Find the $p$-value.
• 15M.1.hl.TZ0.5c: Interpret the $p$-value in the context of the question.

Knowledge of the facts that the regression of $X$ on $Y$ (${\text{E}}(X)|Y = y$) and $Y$ on $X$ (${\text{E}}(Y)|X = x$) are linear.

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Least-squares estimates of these regression lines (proof not required).

• 15M.1.hl.TZ0.5d: Find the equation of the regression line of $y$ on $x$.

The use of these regression lines to predict the value of one of the variables given the value of the other.

• 15M.1.hl.TZ0.5e: Estimate the foot length of a boy of height 170 cm.