8 (Correlation and Diversification) Assume we have two stocks, A and B, show that a particular combination of the two stocks produce a risk-free portfolio when the correlation between the return of A and B is -1.
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- Describe about the Linearity as correlation coefficient assumption.The correlation coefficient between the yearly returns of two mutual funds is 0.20. What does that mean about the strength and direction of the linear relationship between the returns of the two funds?Give examples of two variables that have a perfect positive linear correlation and two variables that have a perfect negative linear correlation.
- Why do we use partial correlations?Suppose a positive linear correlation is found between two quantities. Does this mean that one of the quantities increasing causes the other to increase? If not, what does it mean?One of nature's patterns connects the percent of adult birds in a colony that return from the previous year and the number of new adults that join the colony. Here are data for 10 colonies of sparrowhawks: 81 Percent return, X New adults, Y 74 6 66 52 73 62 52 12 15 16 45 17 62 18 46 18 11 (a) Draw a scatter plot of the data. (b) Find the equation of the least squares regression line for predicting y from x using the information below: n=10 >x, = 613 , Ex = 38959, Ey; = 126, Ey = 1808, Ex,y; = 7333 (Show the details of your work.) X denotes the percent of adult sparrowhawks that return to a colony from the previous year, and Y denotes the number of new adult birds that join the colony.
- Q3 - Returns on stocks X and Y are listed below: Period 1 2 3 4 5 6 7Stock X 3% -2% 9% 6% -1% -4% 11%Stock Y 1% -4% 7% 12% 3% -2% -1% Consider a portfolio of 20% stock X and 80% stock Y. What is the (population) variance of portfolio returns? Please round your answer to six decimal places.At least squares regression equation is y=681.3x+16,062 where you is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.7744. Complete parts (a) through (d). Predict the median income of a region in which 30% of adults 25 years and older have at least a bachelor's degree.A correlation coefficient close to zero is a strong indicator of a positive linear relationship between two variables.
- The least-squares regression equation is y = 618.4x+ 17,572 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a linear relation between the two variables with a correlation coefficient of 0.6761. Complete parts (a) through (d). 55000- 20000- 15 20 25 30 35 40 45 50 55 60 Bachelor's % ..... (a) Predict the median income of a region in which 25% of adults 25 years and older have at least a bachelor's degree. (Round to the nearest dollar as needed.) (b) In a particular region, 29.2 percent of adults 25 years and older, have at least a bachelor's degree. The median income in this region is $38,940. Is this income higher than what you would expect? Why? This is than expected because the expected income is $ (Round to the nearest dollar as needed.) (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do…The least-squares regression equation is y = 753.6x + 12,900 where y is the median income and x is the percentage of 25 years and older with at least a bachelor's degree in the region. The scatter diagram indicates a 55000- linear relation between the two variables with a correlation coefficient of 0.8274. Complete parts (a) through (d). 20000+ 15 20 25 30 35 40 45 50 55 60 Bachelor's % (a) Predict the median income of a region in which 20% of adults 25 years and older have at least a bachelor's degree. (Round to the nearest dollar as needed.) (b) In a particular region, 28.8 percent of adults 25 years and older have at least a bachelor's degree. The median income in this region is $37,925. Is this income higher than what you would expect? Why? This is than expected because the expected income is $ (Round to the nearest dollar as needed.) (c) Interpret the slope. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or decimal. Do not…Over the past 50 years, there has been a strong negative correlation between average annual income and the record time to run 1 mile. In other words, average annual incomes have been rising while the record time to run 1 mile has been decreasing. (b) What lurking variables might be causing the increase in one or both of the variables? Explain your answer.
