LinReg
y= a+bx
a=2.17306922
b=0.32743551
r^2=0.3704382065
r=0.60863635
Write the equation of the least-squares regression line. Use the full accuracy shown in the calculator output (do not round your answers).
5 answers
The least-squares regression line is given by the equation \( y = a + bx \), where \( a \) is the y-intercept and \( b \) is the slope of the line.
From the calculator output:
Substituting these values into the equation, we get:
\[ y = 2.17306922 + 0.32743551x \]
So, the equation of the least-squares regression line is:
\[ y = 2.17306922 + 0.32743551x \]
The correlation between the interest rate and the yield of the stock is represented by the correlation coefficient \( r \). From the calculator output, the value of \( r \) is:
\[ r = 0.60863635 \]
This indicates a positive correlation between the prime interest rate and the yield of the stock. The value of \( r \) can range from -1 to 1, where:
In this case, an \( r \) value of approximately \( 0.6086 \) suggests a moderate positive correlation between the interest rate and the yield of the stock. This implies that, as the interest rate increases, the yield of the stock tends to increase as well.
To predict the price of the stock when the prime interest rate (\( x \)) is 6%, you can substitute \( x = 6 \) into the least-squares regression line equation:
\[ y = 2.17306922 + 0.32743551x \]
Substituting \( x = 6 \):
\[ y = 2.17306922 + 0.32743551(6) \]
Calculating the product:
\[ 0.32743551 \times 6 = 1.96461306 \]
Now, adding it to the y-intercept:
\[ y = 2.17306922 + 1.96461306 = 4.13768228 \]
Therefore, the predicted price when the prime interest rate is 6% is:
\[ \boxed{4.1377} \]
(Rounded to four decimal places.)
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