Question

In: Statistics and Probability

Y X1 X2 X3 21.87838 70.60643 32.53764 16.41044 93.77804 24.77081 92.403 93.99289 72.82208 22.38328 81.0025 34.85534...

Y	X1	X2	X3
21.87838	70.60643	32.53764	16.41044
93.77804	24.77081	92.403	93.99289
72.82208	22.38328	81.0025	34.85534
9.280099	34.70495	26.33653	61.68477
31.1062	61.91305	51.84463	92.25529
92.64739	17.90097	72.9859	44.74383
81.74105	36.03165	79.02588	59.32679
89.92953	21.51851	34.83117	11.82339
78.49144	48.2808	65.38289	27.14759
65.12506	73.91513	45.78317	48.29154
63.9783	42.63024	51.48476	80.61577
23.76638	81.84579	87.52321	47.18775
52.7846	14.18943	23.4629	82.91467
31.50099	90.70568	88.84991	27.21473
45.53072	54.93847	39.86673	86.99951
35.69863	27.72768	80.01956	21.69039
9.978362	58.42174	61.50215	54.04685
94.04123	72.2205	50.09629	66.52428
93.1308	51.50087	12.27189	22.93652
42.10923	68.76678	35.29041	23.17554
8.30253	9.043764	71.03076	26.70983
7.993683	7.451186	86.30393	28.6408
61.24702	31.66482	50.4105	20.05216
13.86984	75.09412	26.66686	76.40739
31.21632	94.43333	62.68383	81.74642
72.60186	13.43745	58.10215	48.42045
43.08142	70.58226	8.592578	12.14566
75.33583	72.40043	12.83587	22.06638
86.41136	30.24949	89.20978	85.65938
86.0864	38.26341	68.98163	60.13248
29.57002	22.18455	52.75237	54.18918
75.3412	32.919	24.846	11.76699
40.81475	42.46641	80.46269	9.629231
60.65081	92.06461	36.30021	28.46623
8.383099	14.21897	55.42189	25.32136
38.21238	18.43272	89.10504	35.03259
71.59474	42.34019	30.41063	72.5186
57.48445	38.01633	54.26438	91.54628
62.92822	63.21558	46.74731	35.85708
86.75781	59.27039	62.37498	62.31858
61.14228	33.42927	8.127964	91.84439
21.7629	87.34864	52.95111	87.89651

Find the correlation coefficients between Y and X1, X2 and X3 and test the significance of population correlation coefficient using the value of r calculated for X2 and X3.
Estimate the regression equation for Y and X1, Y and X2 and report the results and explain the intercept and slope coefficients.
Check the significance or insignificance of the independent variables? and explain the coefficient of determination and standard error of estimate.
Find the predicted value of Y when X1= 20, X2= 30 and X3= 25. Write down first five residuals of the estimated equation.

Expert Solution

1. The correlation coefficient is not significant.

	Y	X1	X2	X3
Y	1.000
X1	-.121	1.000
X2	-.049	-.230	1.000
X3	.063	.063	.036	1.000

2. The regression equation is:

Y = 59.3685 - 0.1341*X1

The relationship is insignificant. (p > .05)

For every increase in X1, the value of Y will decrease by 0.1341.

When X1 is constant, the value of Y will increase by 59.3685.

The regression equation is:

Y = 56.0864 - 0.0560*X2

The relationship is insignificant. (p > .05)

For every increase in X2, the value of Y will decrease by 0.0560.

When X2 is constant, the value of Y will increase by 56.0864.

3. X1 is not significant. (p > .05)

X2 is not significant. (p > .05)

X3 is not significant. (p > .05)

The coefficient of determination is 0.026.

The standard error of the estimate is 28.826.

4. The predicted value of Y is 57.82.

Observation	Y	Predicted	Residual
1	21.87838	48.76989	-26.89151
2	93.77804	56.24570	37.53234
3	72.82208	53.22351	19.59857
4	9.28010	58.60905	-49.32895
5	31.10620	54.08195	-22.97575

orchestra answered 1 year ago

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