Question

For a sample of $\mathbf{2 0}$ monthly observations, a financial analyst wants to regress the percentage rate of return $(Y)$ of the common stock of a corporation on the percentage rate of return $(X)$ of the Standard \& Poor's 500 index. The following information is available: $$ \sum_{i=1}^{20} y_i=22.6 \quad \sum_{i=1}^{20} x_i=25.4 \quad \sum_{i=1}^{20} x_i^2=145.7 \quad \sum_{i=1}^{20} x_i y_i=150.5 $$ a. Estimate the linear regression of $Y$ on $X$. b. Interpret the slope of the sample regression line. c. Interpret the intercept of the sample regression line.

   For a sample of $\mathbf{2 0}$ monthly observations, a financial analyst wants to regress the percentage rate of return $(Y)$ of the common stock of a corporation on the percentage rate of return $(X)$ of the Standard \& Poor's 500 index. The following information is available:
$$
\sum_{i=1}^{20} y_i=22.6 \quad \sum_{i=1}^{20} x_i=25.4 \quad \sum_{i=1}^{20} x_i^2=145.7 \quad \sum_{i=1}^{20} x_i y_i=150.5
$$
a. Estimate the linear regression of $Y$ on $X$.
b. Interpret the slope of the sample regression line.
c. Interpret the intercept of the sample regression line.

Statistics for Business and Economics: Global Edition

Newbold P., Carlson… 8th Edition

Chapter 11, Problem 20

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Step 1

The mean of $X$, denoted as $\bar{x}$, is calculated as: $$ \bar{x} = \frac{\sum_{i=1}^{20} x_i}{20} = \frac{25.4}{20} = 1.27 $$ The mean of $Y$, denoted as $\bar{y}$, is calculated as: $$ \bar{y} = \frac{\sum_{i=1}^{20} y_i}{20} = \frac{22.6}{20} = 1.13 $$ Show more…

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For a sample of $\mathbf{2 0}$ monthly observations, a financial analyst wants to regress the percentage rate of return $(Y)$ of the common stock of a corporation on the percentage rate of return $(X)$ of the Standard \& Poor's 500 index. The following information is available: $$ \sum_{i=1}^{20} y_i=22.6 \quad \sum_{i=1}^{20} x_i=25.4 \quad \sum_{i=1}^{20} x_i^2=145.7 \quad \sum_{i=1}^{20} x_i y_i=150.5 $$ a. Estimate the linear regression of $Y$ on $X$. b. Interpret the slope of the sample regression line. c. Interpret the intercept of the sample regression line.

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