The following table presents monthly interest rates, in percent, for 30 year and- 15 year fixed-rate mortgages, for a recent year.30 Year      15 year            30 year           15 year3.92            3.20                 3.55                2.853.89            3.16                  3.60                2.863.95            3.20                  3.47                2.783.91            3.14                  3.38               2.693.80            3.03                  3.35               2.663.68            2.95                  3.35                2.66a. Construct a scatter plot of the 15- year rate (y) versus the 30-year rate (x).b. Compute the correlation coefficient between 30-year and 15-year rates.

Question
Asked Sep 23, 2019
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The following table presents monthly interest rates, in percent, for 30 year and- 15 year fixed-rate mortgages, for a recent year.

30 Year      15 year            30 year           15 year

3.92            3.20                 3.55                2.85

3.89            3.16                  3.60                2.86

3.95            3.20                  3.47                2.78

3.91            3.14                  3.38               2.69

3.80            3.03                  3.35               2.66

3.68            2.95                  3.35                2.66

a. Construct a scatter plot of the 15- year rate (y) versus the 30-year rate (x).

b. Compute the correlation coefficient between 30-year and 15-year rates.

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Expert Answer

Step 1
  1. Scatterplot of the 15-year rate (y) versus the 30-year rate (x).

Software Procedure:

Step-by-step software procedure to draw scatter plot using Excel software is given below:

  • Open an EXCEL file.
  • In column A and B, the 30-year and 15-year data were entered.
  • Select the data > click on insert.
  • Chose X Y (Scatter) from chart.
  • Click OK.
  • Click on the data points>right click> add trend line.
  • Choose

The scatterplot of the data obtained using software is given below:

Scatter plot for 15-year (y) versus 30-year (x)
3.5
3
2.5
2
1.5
1
0.5
0
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
30-year
15-year
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Image Transcriptionclose

Scatter plot for 15-year (y) versus 30-year (x) 3.5 3 2.5 2 1.5 1 0.5 0 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 30-year 15-year

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Step 2

In the scatterplot, if the points lie along the straight line then there exists a linear relationship between the variables x and y.

Step 3

b. Correlation coefficient between 30-year rate and 15-year rate:The sample correlation coefficient can be obtained using EXCEL. Enter the values of x and y in two columns, say in columns A2:A13 and B2:B13 in an EXCEL sheet. I...

fx
CORREL(A2:A13, B2:B13)
F
G
H
0.996344
LL
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Image Transcriptionclose

fx CORREL(A2:A13, B2:B13) F G H 0.996344 LL

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