When analyzing a particular stock's performance (y) compared to the performance of a related benchmark segment of the stock market (x), the slope is a relative risk measurement. The slope depicts a fund's volatility against the benchmark. Many financial analysts calculate the slopes for stock funds using the S&P 500 Index as the benchmark.

This market model assumes that the rate of return of a stock (y) is linearly related to the rate of return (x) of the benchmark:

y = b₀ + b₁x.

In this context the slope b₁ is usually referred to as the beta coefficient of the stock. Beta is explained at most business-oriented web sites, see for example Morningstar.

• Interpretation of beta
• b₁ = 1 means the stock's rate of return moves up and down in perfect harmony with the benchmark market.
• b₁ > 1 means the stock's rate of return is more sensitive to changes in the level of the benchmark market than is the average stock.
• 0 b₁

Investors with a high tolerance for risk like b₁ > 1; they can earn more if the overall market improves slightly, but lose more if the market declines even a small amount. Investors with a low tolerance for risk like 0b₁

For example, Texaco has a beta coefficient of 0.44, which means that when the overall market rate of return changes by 1%, Texaco's rate of return changes only 0.44%. So Texaco doesn't move much at all relative to the overall market. An investor with a low tolerance for risk would be attracted to Texaco because its beta coefficient is less than 1.

What does r² mean?

In this setting r² measures the proportion of the total risk in the particular stock related to the benchmark market and 1 - r² measures the proportion of the total risk that is related to specific company-related events and decisions.

DO THE FOLLOWING:

Apply the market model to the Standard and Poor's Composite Index (the x-variable) and the monthly returns of Intel (the y-variable) for a recent 4-year period, which are stored in columns 1 and 2, respectively, in this Excel file

What is the value of the test statistic for the hypothesis test H₀: b₁ = 0, H_a: b₁ 0?

What is the P-value for the hypothesis test H₀: b₁ = 0, H_a: b₁ 0?

INDEX 0.007291 0.013532 0.021217 -0.024523 0.026318 0.003479 -0.004986 0.037531 -0.007638 0.019717 -0.008966 0.01219 0.033612 -0.02683 -0.043453 0.012034 0.017335 -0.024921 0.032639 0.041427 -0.024118 0.022596 -0.036316 0.014704 0.025741 0.039381 0.029446 0.029453 0.039665 0.024231 0.032912 0.003592 0.041988 -0.003627 0.044155 0.017771 0.035422 0.009802 0.009289 0.014987 0.025321 0.004278 -0.044581 0.021952 0.056061 0.027435 0.076412 0.0143608 INTEL 0.228084 0.091335 -0.012876 -0.171879 0.165572 -0.007892 -0.049102 0.229665 0.101167 -0.105306 -0.027668 0.00813 0.053246 0.05364 -0.018182 -0.095578 0.02459 -0.064 0.013969 0.109705 -0.064639 0.011173 0.016097 0.011881 0.087031 0.14955 0.064263 0.206922 0.096459 0.128062 0.027265 -0.055769 -0.01833 0.160416 -0.128801 -0.067762 -0.025988 0.064781 -0.032944 0.191908 0.114391 -0.027318 0.023666 0.062396 0.195771 0.151816 0.154721 0.043056 INDEX 0.007291 0.013532 0.021217 -0.024523 0.026318 0.003479 -0.004986 0.037531 -0.007638 0.019717 -0.008966 0.01219 0.033612 -0.02683 -0.043453 0.012034 0.017335 -0.024921 0.032639 0.041427 -0.024118 0.022596 -0.036316 0.014704 0.025741 0.039381 0.029446 0.029453 0.039665 0.024231 0.032912 0.003592 0.041988 -0.003627 0.044155 0.017771 0.035422 0.009802 0.009289 0.014987 0.025321 0.004278 -0.044581 0.021952 0.056061 0.027435 0.076412 0.0143608 INTEL 0.228084 0.091335 -0.012876 -0.171879 0.165572 -0.007892 -0.049102 0.229665 0.101167 -0.105306 -0.027668 0.00813 0.053246 0.05364 -0.018182 -0.095578 0.02459 -0.064 0.013969 0.109705 -0.064639 0.011173 0.016097 0.011881 0.087031 0.14955 0.064263 0.206922 0.096459 0.128062 0.027265 -0.055769 -0.01833 0.160416 -0.128801 -0.067762 -0.025988 0.064781 -0.032944 0.191908 0.114391 -0.027318 0.023666 0.062396 0.195771 0.151816 0.154721 0.043056