Consider the following model y = β0 + β1x + ∈, where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 2007, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of 1 is shown to the right of each least squares prediction equation. Estimated Market Model & Estimated Std Error of β1 Company A y = .0010 + 1.40x, β1 = .03 Company B y = .0005 - 1.21x, β1 = .06 Company C y = .0010 + 1.62x 1.34, β1 = 1.34 Company D y = .0013 + .76x .15, β1 = 0.15 Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock. a) 161.6 b) 1.40 ± .067 c) 1.40 d) 46.7
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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Consider the following model y = β0 + β1x + ∈, where y is the daily rate of return of a stock, and x is the daily rate of return of the stock market as a whole, measured by the daily rate of return of Standard & Poor's (S&P) 500 Composite Index. Using a random sample of n = 12 days from 2007, the least squares lines shown in the table below were obtained for four firms. The estimated standard error of 1 is shown to the right of each least squares prediction equation. |
Estimated Market Model & Estimated Std Error of β1
Company A y = .0010 + 1.40x, β1 = .03
Company B y = .0005 - 1.21x, β1 = .06
Company C y = .0010 + 1.62x 1.34, β1 = 1.34
Company D y = .0013 + .76x .15, β1 = 0.15
Calculate the test statistic for determining whether the market model is useful for predicting daily rate of return of Company A's stock.
a) 161.6
b) 1.40 ± .067
c) 1.40
d) 46.7
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