Question

Phys Sci 1.2.23 The relationship between the length of a pendulum L and the time for one complete oscillation can be determined from the data in the table to the night the horizontal and as the vertical Does it seem to the data? a. Find the least squaresine equation and graph it simultaneously with the data points with b. Find the correlation coefficient and interpretit. Does it confirm your answer to parta? glass L2335 a. Find the least squares line equation The equation of the last squares line is Y (Type an expression using as the variable. Use r s or decimals for any numbers in the expression. Round to the decimal places as needed.)

Answer 1

a)

as let regression line ŷ = ât in then using least squares method I min s - 20 - 9 2 - 2 2 (y - 2 - 6 mj² == -26%: -20) Imst nr 2 a- b 2 L 1= an {.4 - an- bun.=0 1971 L=1 is an a= TE yi- b E ni nis i=1 Bell a = - -, (4;-a-C:) * - ab nn nh an - 4 2 -bE n - nnn 2 -bn) {n -6 { thao 1=1 D 30* - ) , Li-) a 1=1 b = ali-5you Yi-y) ni ninni

	L(ft) (X)	T(sec) (y)	X-Xbar	y-ybar	Sxx	Sxy	y^
	1	1.13	-1.5	-0.58857	-1.5	-0.58857	1.227143
	1.5	1.36	-1	-0.35857	-1.5	-0.53786	1.390952
	2	1.57	-0.5	-0.14857	-1	-0.29714	1.554762
	2.5	1.76	0	0.041429	0	0.103571	1.718571
	3	1.92	0.5	0.201429	1.5	0.604286	1.882381
	3.5	2.08	1	0.361429	3.5	1.265	2.04619
	4	2.21	1.5	0.491429	6	1.965714	2.21
sum	17.5	12.03					6.632857
average	2.5	1.718571
	a^	0.899524
	b^	0.327619

2.5 y = 0.3593x +0.8204 Tisec) T(sec) – Predicted ......... Linear (T(sec)) +o 1 1 2 3 4 5 Lift)

b)

Correlation coefficient b^ = 0.327619

It shows change of rate in T(sec) at one unit change in L(ft)

a)

Least Square line equation

Y = 899524 + 0.327619X