Question

Let x = boiler steam pressure in 100 lb/ in² and let y = critical sheer strength of boiler plate steel joints in tons/ in². We have the following data for a series of factory boilers.

x	4	5	6	8	10
y	3.4	4.2	6.3	10.9	13.3

(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 decimal places.)

y'	=	+  x'
r	=

(c) Use the results of part (b) to find estimates for α and β in the power law y = αx^β. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. (Use 3 decimal places.)

α	=
β	=
	=	· x^

Answer 1

(b) Using Excel we have found equation of regression line:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.990672
R Square	0.981431
Adjusted R Square	0.975241
Standard Error	0.040266
Observations	5

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-0.45119	0.102786	-4.38959	0.021902	-0.7783	-0.12408	-0.7783	-0.12408
log(X)	1.599913	0.127058	12.59195	0.00108	1.195556	2.004269	1.195556	2.004269

herefore, we find that the regression equation is:

log(Y) = -0.451 + 1.600*log(X)

i.e. Y'=-0.451 + 1.600 *X'

from above table we can find correlation coefficient.

Multiple R. This is the correlation coefficient. It tells you how strong the linear relationship

Hence correlation coefficient is 0.991.

(c) Use the results of part (b) to find estimates for ?and ? in the power law y = ?x?. Write the power equation for the relationship between steam pressure and sheer strength of boiler plate steel. (Use 3 decimal places.)

function value

mean of x= 0.783

mean of y =0.790

correlation coefficient r= 0.991

? =1.161

? =1.580

?=1.161*x1.580

NOTE:If you satisfy with this solution please give me a thumb up. Thank-you :)