In the linear regression model with n sample points (m1,91),...(Xn, Jn), the best fit lineis given by y = a + bx wheren*Στι-(2») (Στ)Σrigii=1i=1b=i=1and a = y-br.2nnnΣ - (Σri=1The estimated y-value is given by ji = a + bri. Prove the ff.n(2) Σy = Σi=1i=ln(b) Σ(y. – 9:); = 0.-i=1(c) SST = SSR + SSE [see lecture 12 for definition.](Hint: Expand both LHS and RHS then add/subtract missing terms.)

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Answered: In the linear regression model with n…

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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Forest Fires and Acres Burned Numbers (in thousands) of forest fires over the year and the number (in hundred thousands) of acres burned for 6 recent years are shown. The regression line equation is =y′+−45.79501.34704x. The correlation coefficient is =r0.858. Compute the standard error of the estimate rounded to at least two decimal places, if appropriate. Assume =α0.05 The standard error of the estimate should or should not be calculated. S est= Number of fires x 57 45 72 69 58 47 Number of acres burned y 30 15 62 42 19 26
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A fuel company wants to find the functional relation between the amount of gas it sells for heating and the daily temperature. Given the values for 10 observations ∑x= - 50, ∑x^2 = 626, ∑y^2 = 6432 ∑y= 222, ∑xy= —1743 for the daily average temperature and gas sales (in thousand liters). a) Obtain and interpret the correlation coefficient for the variables.b) Set up the regression equation and interpret the coefficients.c) Find R2 and interpret.d) When the temperature is 10 degrees, please observe the gas sales amount.
There is a relationship in the form of Y = 1 / (a * x ^ b) (x ^ b: means x over b).a) Calculating the correlation coefficient and interpreting the degree of relationship?b) Estimating the y value for x = 4.3 and the x value for y = 0.90 by obtaining the regression equation
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Suppose that you run a correlation and find the correlation coefficient is 0.338 and the regression equation is ˆy=−12.7+4.3xy^=-12.7+4.3x.The mean for the xx data values was 7, and the mean for the y data values was 17.A T Test for the slope of the regression line is performed, and the p-value is greater than the level of significance of 0.05. Use the appropriate method to predict the y value when x is 4.4.
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