! 2. Find a data set of economic/financial time series with one y variable and two independentvariables xi and x2. Verify the following resultR =1-rwhere: R is for the regression of y on both xı and xi; and r are for the regressions ofy onxıand x2, respectively; and r12 is the correlation coefficient between x, and x2.

Lett’s start with a simple example where the goal is to predict the stock_index_price (y) of a…

Answered: 2. Find a data set of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following correlations -0.9 , -0.5 , -0.2 , 0 , 0.2 , 0.5 and 0.9. For each give the fraction of the variation in y that is explained by the least-squares regression of y on x.
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?
If a sample of 25 pairs of data yields a correlation coefficient, r, of 0.390 and the scatterplot displays a linear trend, can you use the regression equation to make predictions, assuming your x-values are within the domain of the data set? Choose your answer from the multiple choice answers below A.) Yes, because rcrit = 0.396 and the regression coefficient, r, is less than this value. B.) Yes, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. C.) No, because rcrit = 0.381 and the regression coefficient, r, is greater than this value. D.) No, because rcrit = 0.396 and the regression coefficient, r, is less than this value.
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 70 30 1995 130 40 110 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = (b) Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.
The following table shows the number of fiber optic cable connections to homes in a country from 2000 to 2004 (t = 0 represents 2000). Year t 0 1 2 3 4 Connections c (Thousands) 5 15 30 70 155 (a) Use technology to obtain the linear regression line and the correlation coefficient r, with all coefficients rounded to two decimal places. c(t) = r =
he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a) With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =
9)Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 11 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.79, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 79000 and the sum of squared errors (SSE) is 21000. From this information, what is the adjusted R-square? .8 .7 NONE OF THE OTHERS .6 .5
17) Suppose that Y is normal and we have three explanatory unknowns which are also normal, and we have an independent random sample of 41 members of the population, where for each member, the value of Y as well as the values of the three explanatory unknowns were observed. The data is entered into a computer using linear regression software and the output summary tells us that R-square is 0.9, the linear model coefficient of the first explanatory unknown is 7 with standard error estimate 2.5, the coefficient for the second explanatory unknown is 11 with standard error 2, and the coefficient for the third explanatory unknown is 15 with standard error 4. The regression intercept is reported as 28. The sum of squares in regression (SSR) is reported as 90000 and the sum of squared errors (SSE) is 10000. From this information, what is the number of degrees of freedom for the t-distribution used to compute critical values for hypothesis tests and confidence intervals for the individual…
The following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 120 40 2000 330 130 280 120 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) =
In a typical multiple linear regression model where x1 and x2 are non-random regressors, the expected value of the response variable y given x1 and x2 is denoted by E(y | 2,, X2). Build a multiple linear regression model for E (y | *,, *2) such that the value of E(y | x1, X2) may change as the value of x2 changes but the change in the value of E(y | X1, X2) may differ in the value of x1 . How can such a potential difference be tested and estimated statistically?

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