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.

Step 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:

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...

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