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According to the given information, the percent change in security A's price that can be explained by changes in the market is 64%.
The correlation coefficient between security a and the market is 0.80
The percent change in security a's price that can be explained by changes in the market = [tex]0.8^2[/tex] = 0.64 = 64%
The coefficient of determination (R squared), which measures how well two variables correlate, is 0.80. As a result, only 64% of investment returns can be accounted for by changes in the market (systematic risk accounts for the remaining 64%).
- The strength of associations between data variables is evaluated using correlation coefficients.
- The most widely used indicator, known as a Pearson correlation coefficient, assesses the strength and direction of a linear relationship between two variables.
- Always, values fall within the range of -1 for a perfectly inverse relationship and 1 for a perfectly positive correlation. A linear relationship or a very weak correlation is indicated by values that are zero or very close to zero.
- Depending on the application, certain coefficient values may be necessary to indicate a significant association. In the case of a normal population distribution, the correlation coefficient and sample size can be used to determine the correlation's statistical significance.
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