Question

In: Statistics and Probability

he data shown below for the dependent​ variable, y, and the independent​ variable, x, have been...

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.

Solutions

Expert Solution

(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.


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