Question

11. 0.13/1 points 1 Previous Answers BBUnderStat 12 9.2.025 My Notes Ask Your Teacher Let x = boiler steam pressure in 1001b/in2 and let y = critical sheer strength of boler plate steel onts in tor sin2, we have the following data for a series of factory boilers 10 .4 4.2 6.3 10.9 13.3 (a) Make the logarithmic transformations x' log (x) and y' equation seem to be a good fit to this plot? log (v). Then make a scatter plot of the (x, y) values. Does a linear 0 The transformed data does not fit a straight line well. The data seem to explode as x decreases. The transformed data fit a straight line well. O The transformed data does not fit a straight line well. The data seem to have a parabolic shape. O The transformed data does not fit a straight line well. The data seem to explode as x increases. (b) Use the (x, y) data points and a calculator with regression keys to find the least-squares equation y' - a + bx: What is the correlation coefficient? (Use 3 decaimal places.) (c) Use the results of part (b) to find estimates for α and the power law y-an, write the power equation for the relationship between steam pressure and sheer strength of boler plate steel. (Use 3 decimal places.)

Answer 1

Regression equation:

X*Y 13.6 21 37.8 87.2 133 292.6 11.56 17.64 39.69 118.81 176.89 364.59 16 25 36 64 100 241 6.3 10.9 13.3 38.1 10 Sum Based on the above table, the following is calculated 6.6 x, 38.1 7.62 X241 -332/5 23.2 DY) -364.59 38.12/5= 74.268 SSY Y= ΣΥ2 33×38.1/5= 41.14 YI-292.6

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y- intercept n) are obtained as follows SSxy41.14 SSx.x2.2 1.7733 SSx 23.2 n-Y _ X . m-7.62 _ 6.6 x 1.7733 _ 4.0836 Therefore, we find that the regression equation is: Y--4.08361.7733X

Rsquare = 0.9822 (Calculator result)