# Statistics- MIDTERM 2 You find the following return characteristics

## Statistics- MIDTERM 2 You find the following return characteristics

MIDTERM 2You find the following return characteristics of two ETFs:i. The ETF y has a monthly expected return of -4.2% and a monthly stdev of 20%ii. The ETF x has a monthly mean return of 1% and a monthly stdev of 5%iii. The correlation between the two ETFs is -0.8 (negative 0.8)Q1. If you run a regression of return on ETF_ y on ETF_x, what is the regression slope and regressionintercept?RET_y =a+ b * ret_x + errorQ1b. What is the standard deviation of the forecast , ie ret_y_forecast = a+b*ret_x ?Q1c. What is the standard deviation of the forecast error, ie error=ret_y â ret_y_forecast?Q1d. How much of a variation in ETF_yâs return can be explained by ETF_ x?(HINT: what is the R -square of the regression?)Q2.After surveying 400 students at XYZ University you find out that 300 students support the proposalfor a student housing project bear XYZ campus.a. What are the two standard deviation error bands for you point estimate?b. Based on your survey, what is the chance that the proposal will be defeated in general vote?c. If want to shrink the standard deviation of your survey to 1% how many people do you need to survey?

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