• 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 \(\rho \).

None

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.