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In: Finance

Using the following 5 year data series, calculate the correlation between interest rates and US new...

Using the following 5 year data series, calculate the correlation between interest rates and US new home sales.

Year Home sales (thousands) Interest rate (%)
1 520 8
2 673 5
3 631 3
4 581 8
5 658 10

The answer is -.263

Please show how to get there

Solutions

Expert Solution

  • Let 'x' be the data set of home sales & 'y' be the data set of interest rates.
  • Find the mean of x (let it be x̄) and the mean of y (let it be ȳ).
    • x
      1 520
      2 673
      3 631
      4 581
      5 658
      Sum of x 3063
    • Mean 'x̄' = Sum of the terms/number of terms = 3063 ÷ 5 = 612.6
    • y
      1 8
      2 5
      3 3
      4 8
      5 10
      Sum of y 34
    • Mean 'ȳ' = Sum of the terms/number of terms = 34 ÷ 5 = 6.8
  • Subtract mean from each value in the data series. i,e, find (x - x̄) & (y - ȳ)
  • FInd covariance of both 'x' & 'y': Cov(x, y) = [Σ(x - x̄) * (y - ȳ)] / n = -182.4/5 = -36.48
  • Find standard deviation of x and y.
    • Standard deviation (σx) = √Σ(x - x̄)2/n = √15621.2/5 = √3124.24 = 55.8949
    • Standard deviation (σy) = √Σ(y - ȳ)2/n = √30.8/5 = √6.16 = 2.481935
  • Correlation between x & y = Cov (x, y) ÷ (σx *σy) = -36.48 ÷ (55.8949 * 2.481935) = -36.48 ÷ 138.7275 = -0.263

jeff jeffy answered 1 year ago
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