Effect of data transformation on correlation

A question is this type if and only if it asks about how linear transformations or coding of variables affects correlation or regression.

2 questions · Moderate -0.6

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AQA S1 2013 June Q1
7 marks Moderate -0.8
1 The average maximum monthly temperatures, \(u\) degrees Fahrenheit, and the average minimum monthly temperatures, \(v\) degrees Fahrenheit, in New York City are as follows.
JanFebMarAprMayJunJulAugSepOctNovDec
Maximum (u)394048617181858377675441
Minimum (v)262734445363686660514130
    1. Calculate, to one decimal place, the mean and the standard deviation of the 12 values of the average maximum monthly temperature.
    2. For comparative purposes with a UK city, it was necessary to convert the temperatures from degrees Fahrenheit ( \({ } ^ { \circ } \mathrm { F }\) ) to degrees Celsius ( \({ } ^ { \circ } \mathrm { C }\) ). The formula used to convert \(f ^ { \circ } \mathrm { F }\) to \(c ^ { \circ } \mathrm { C }\) is: $$c = \frac { 5 } { 9 } ( f - 32 )$$ Use this formula and your answers in part (a)(i) to calculate, in \({ } ^ { \circ } \mathbf { C }\), the mean and the standard deviation of the 12 values of the average maximum monthly temperature.
      (3 marks)
  2. The value of the product moment correlation coefficient, \(r _ { u v }\), between the above 12 values of \(u\) and \(v\) is 0.997 , correct to three decimal places. State, giving a reason, the corresponding value of \(r _ { x y }\), where \(x\) and \(y\) are the exact equivalent temperatures in \({ } ^ { \circ } \mathrm { C }\) of \(u\) and \(v\) respectively.
    (2 marks)
Edexcel S1 2023 June Q2
13 marks Moderate -0.3
Two students, Olive and Shan, collect data on the weight, \(w\) grams, and the tail length, \(t\) cm, of 15 mice. Olive summarised the data as follows \(S_tt = 5.3173\) \quad \(\sum w^2 = 6089.12\) \quad \(\sum tw = 2304.53\) \quad \(\sum w = 297.8\) \quad \(\sum t = 114.8\)
  1. Calculate the value of \(S_{ww}\) and the value of \(S_{tw}\) [3]
  2. Calculate the value of the product moment correlation coefficient between \(w\) and \(t\) [2]
  3. Show that the equation of the regression line of \(w\) on \(t\) can be written as $$w = -16.7 + 4.77t$$ [3]
  4. Give an interpretation of the gradient of the regression line. [1]
  5. Explain why it would not be appropriate to use the regression line in part (c) to estimate the weight of a mouse with a tail length of 2cm. [2]
Shan decided to code the data using \(x = t - 6\) and \(y = \frac{w}{2} - 5\)
  1. Write down the value of the product moment correlation coefficient between \(x\) and \(y\) [1]
  2. Write down an equation of the regression line of \(y\) on \(x\) You do not need to simplify your equation. [1]