Question

he data shown below for the dependent​ variable, y, and the independent​ variable, x, have been collected using simple random sampling.

x	10		14	17	11	19	18	17	14	17	18
y	120		140	190	140	190	180	180	160	170	190
.a.		Develop a simple linear regression equation for these data.
.b.		Calculate the sum of squared​ residuals, the total sum of​squares, and the coefficient of determination.
.c.		Calculate the standard error of the estimate.
.d.		Calculate the standard error for the regression slope.
.e.		Conduct the hypothesis test to determine whether the regression slope coefficient is equal to 0. Test using alphaαequals=0.10.

Answer 1

(a)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	10	120	100	14400	1200
	14	140	196	19600	1960
	17	190	289	36100	3230
	11	140	121	19600	1540
	19	190	361	36100	3610
	18	180	324	32400	3240
	17	180	289	32400	3060
	14	160	196	25600	2240
	17	170	289	28900	2890
	18	190	324	36100	3420
Total	155	1660	2489	281200	26390

(b)

The coefficient of determination is

(c)

(d)

(e)

Conclusion: There is no evidence to conclude that the regression slope coefficient is equal to 0.