1. Using the formulas for method of least square in lecture # 4 to find the...

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1. Using the formulas for method of least square in lecture # 4 to find the equation of the linear regression line y = a + ax, correlation coefficient, and standard error for the following data set of x and y. (20 points) X 12.3 17.8 22.5 -13.9 -16.5 -17.3 24.7 29.2 33.3 34.8 -20.5 -22.4 -23.8 -27.6 2. A student wants to make a short cut in finding the equation ya+ax for the above data set by using only two data points (x=12.3, y=-13.9) and (x=34.8, y=-27.6). a. What are the values of ao and a1? b. What are the values of correlation coefficient and standard error? Explain your answer if the results for question 2 are not the same as the results for problem #1. 3. Transform the below equation into the linear form Y=ao+a1X. y = K 10 (bx) Specify Y, a0, a1, and X. y = a + ax (15 points) (10 points) a. = x-nx a = nxy-xy (x - ( x ) \ -(x)) (x-x) (y- y) 1-1 1 = (n-1)s,sy (x)-nx (v-as-ax) SE= 11-2 1. Using the formulas for method of least square in lecture # 4 to find the equation of the linear regression line y = a + ax, correlation coefficient, and standard error for the following data set of x and y. (20 points) X 12.3 17.8 22.5 -13.9 -16.5 -17.3 24.7 29.2 33.3 34.8 -20.5 -22.4 -23.8 -27.6 2. A student wants to make a short cut in finding the equation ya+ax for the above data set by using only two data points (x=12.3, y=-13.9) and (x=34.8, y=-27.6). a. What are the values of ao and a1? b. What are the values of correlation coefficient and standard error? Explain your answer if the results for question 2 are not the same as the results for problem #1. 3. Transform the below equation into the linear form Y=ao+a1X. y = K 10 (bx) Specify Y, a0, a1, and X. y = a + ax (15 points) (10 points) a. = x-nx a = nxy-xy (x - ( x ) \ -(x)) (x-x) (y- y) 1-1 1 = (n-1)s,sy (x)-nx (v-as-ax) SE= 11-2