Identify errors in correlation analysis

6

1. A student calculated the values of the product moment correlation coefficient, \(r\), and Spearman's rank correlation coefficient, \(r _ { s }\), for two sets of bivariate data, \(A\) and \(B\). His results are given below. $$\begin{array} { l l } A : & r = 0.9 \text { and } r _ { s } = 1
   B : & r = 1 \quad \text { and } r _ { s } = 0.9 \end{array}$$ With the aid of a diagram where appropriate, explain why the student's results for \(A\) could both be correct but his results for \(B\) cannot both be correct.
2. An old research paper has been partially destroyed. The surviving part of the paper contains the following incomplete information about some bivariate data from an experiment.
   \includegraphics[max width=\textwidth, alt={}, center]{5c25d6cf-2c23-4b49-88fb-e4abe6c281e4-4_339_1200_1117_511} Calculate the missing constant at the end of the equation of the second regression line.

2 Dr Hanna has a special clinic for her older patients. She asked a medical student, Lenny, to select a random sample of 25 of her male patients, aged between 55 and 65 years, and, from their clinical records, to list their heights, weights and waist measurements. Lenny was then asked to calculate three values of the product moment correlation coefficient based upon his collected data. His results were:

1. 0.365 between height and waist measurement;
2. 1.16 between height and weight;
3. - 0.583 between weight and waist measurement. For each of Lenny's three calculated values, state whether the value is definitely correct, probably correct, probably incorrect or definitely incorrect.

12 Manny is studying the price and number of pages of a random sample of books.
He calculates the value of the product moment correlation coefficient between the price and number of pages in each book as 1.05 Which of the following best describes the value 1.05 ?
Tick ( \(\checkmark\) ) one box.
definitely correct □
probably correct □
probably incorrect □
definitely incorrect □
\includegraphics[max width=\textwidth, alt={}, center]{b45dc98e-1699-47c9-9228-5abe0e5c9195-15_2488_1716_219_153}

10 Anke has collected data from 30 similar-sized cars to investigate any correlation between the age of the car and the current market value. She calculates the correlation coefficient. Which of the following statements best describes her answer of - 1.2 ?
Tick ( \(\checkmark\) ) one box. Definitely incorrect □ Probably incorrect
\includegraphics[max width=\textwidth, alt={}, center]{0abb6343-017d-4629-8a2d-cfb405dc2d14-16_108_113_1265_959} Probably correct
\includegraphics[max width=\textwidth, alt={}, center]{0abb6343-017d-4629-8a2d-cfb405dc2d14-16_106_113_1400_959} Definitely correct □

10 Which of the following is not a possible value for a product moment correlation coefficient? Circle your answer. $$- \frac { 6 } { 5 } \quad - \frac { 3 } { 5 } \quad 0$$