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The following display from the TI-84 Plus calculator presents the least-squares regression line for predicting the price of a certain stock (y) from the prime interest rate in percent (x).

LinReg
y= a+bx
a= 1.63395022
b=0.33014339
r^2= 0.384401488
r=0.6200012

What is the regression line equation

5 answers

The least-squares regression line can be expressed in the form \( y = a + bx \), where:

  • \( a \) is the y-intercept,
  • \( b \) is the slope of the line,
  • \( x \) is the independent variable (the prime interest rate in percent),
  • \( y \) is the dependent variable (the price of the stock).

From the display you provided:

  • \( a = 1.63395022 \)
  • \( b = 0.33014339 \)

Substituting these values into the regression line equation gives:

\[ y = 1.63395022 + 0.33014339x \]

This is the equation of the regression line.

What is the correlation between the interest rate and the yield of the stock?

The correlation between the interest rate and the yield of the stock can be determined from the correlation coefficient \( r \), which is provided in the display:

  • \( r = 0.6200012 \)

The correlation coefficient \( r \) ranges from -1 to 1. A value of \( r = 0.6200012 \) indicates a moderate positive correlation between the prime interest rate and the yield of the stock. This means that, generally, as the prime interest rate increases, the yield of the stock tends to increase as well. However, the correlation is not strong, so there are likely other factors influencing the relationship between these two variables.

Predict the price when the prime interest rate is 6%. Round the answer to at least four decimal places.

To predict the price of the stock when the prime interest rate (\( x \)) is 6%, we can use the regression line equation:

\[ y = 1.63395022 + 0.33014339x \]

Substituting \( x = 6 \):

\[ y = 1.63395022 + 0.33014339 \times 6 \]

Calculating the second term:

\[ 0.33014339 \times 6 = 1.98086034 \]

Now, adding this value to the intercept:

\[ y = 1.63395022 + 1.98086034 = 3.61481056 \]

So, the predicted price of the stock when the prime interest rate is 6% is:

\[ \boxed{3.6148} \]

(Rounded to four decimal places.)