11.Define the correlation coefficient ry between the variables x, y.хуShow that r will be positive or negative according asOxy > or < 6x – y-Given x= 4y + 5, y = kx + 4 are the regression lines of x on y and y onx respectively, show that 0sks. If k= find the means of the twoIf k =4'variables and the coefficient of correlation between them.

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Answered: 11. Define the correlation coefficient…

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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Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.04, standard error for the coefficient of z is 0.01, and the sample size is 20. Can we conclude that advertising expenditure is a statistically significant variable?
I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?
1. Suppose that the sales of a company (Y) is regressed on advertising expenditure (x) and labor cost (z), and the estimated regression equation is Y = 5 + 0.5x + 0.7z + u (where u is the error term). Here, sales, advertising expenditure and labor cost are measured in million Tk. Standard error for the coefficient of x is 0.4, standard error for the coefficient of z is 0.01, and the sample size is 20. Based on this information, find out whether labor cost is a statistically significant variable using an appropriate statistical test.
In running a regression of the retunrs of stock XYZ against the returns on the market, the Std for the returns of stock XYZ is 20% and that of the market returns is 15%. If the estimated beta is found to be 0.75 : What is the maximum possible value of beta given that the standar deivation of the returns of stock XYZ is 20% and those of the market is 15% ?
A sample of 7070 women is obtained, and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.2210.221 and the equation of the regression line is ModifyingAbove y with caret equals 17.6 plus 0.940 xy=17.6+0.940x, where x represents height. The mean of the 7070 heights is 62.862.8 in and the mean of the 7070 pulse rates is 77.377.3 beats per minute. Find the best predicted pulse rate of a woman who is 7474 in tall. Use a significance level of alpha equals 0.05α=0.05. The best predicted pulse rate of a woman who is 7474 in tall is nothing beats per minute.
8)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 0.86, 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 86000 and the sum of squared errors (SSE) is 14000. From this information, what is MSE/MST? .5000 NONE OF THE OTHERS .2000 .3000 .4000
Suppose IQ scores were obtained from randomly selected twins. For 20 such pairs of people, the linear correlation coefficient is 0.930 and the equation of the regression line is y=−10.69+1.11x, where x represents the IQ score of the twin born first. Also, the 20 x values have a mean of 98.28 and the 20 y values have a mean of 98.5. What is the best predicted IQ of the twin born second, given that the twin born first has an IQ of 92? Use a significance level of 0.05.LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r.Question content area bottomPart 1The best predicted IQ of the twin born second is enter your response here.(Round to two decimal places as needed.)
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The following table gives the marks obtained by 10 students in POLI 344 (X) together with the marks obtained in the exam in POLI 308 (Y). POLI 344 (X)8 8 9 10 10 11 12 13 13 11 14 POLI 443 (Y) 7 11 8 7 12 11 10 12 14 17 15 (i) State the two equation lines of the regression line. (ii) If a student was absent from POLI 443 but scored 18 in POLI 344 (X) state the regression line, which would be suitable for estimating his/her possible mark in POLI 443 and work out a fair estimate for his /her possible mark.
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
If x and y in a regression model are totally unrelated, _______. the coefficient of determination would be 0 the MSE would be 0s the SSE would be 0 the correlation coefficient would be -1 the coefficient of determination would be 1

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11. Define the correlation coefficient ry between the variables x, y. will be positive or negative according as Show that Oxy > or < Ox-y. Given x= 4y + 5, y = kx + 4 are the regression lines of x on y and y on x respectively, show that 0