Question

Use the data set which is labeled below and answer using regression output in excel

i. 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.

ii. Estimate the regression equation for Y and X1, Y and X2 and report the results and explain the intercept and slope coefficients.

iii. Check the significance or insignificance of the independent variables? and explain the coefficient of determination and standard error of estimate.

iv. Find the predicted value of Y when X1= 20, X2= 30 and X3= 125. Write down first five residuals of the estimated equation.

Y	X1	X2	X3
33.4283	32.96268	16.92215	30.06201
28.97037	7.616413	56.9856	36.19529
14.42695	59.20676	38.73281	3.194128
68.30308	9.144719	71.65822	41.90527
36.60967	39.26304	49.15915	67.94662
34.50435	35.52693	20.51122	45.46315
16.17359	48.01627	61.08484	57.07025
12.12781	62.64879	17.2385	19.76266
41.56441	17.74422	49.82528	71.12354
57.93912	12.90088	16.6303	58.51167
30.42961	37.25575	4.753624	31.63265
8.420667	40.63094	53.26063	25.18525
52.69253	39.63063	63.03867	9.87991
26.43062	60.18702	51.28675	50.65404
5.769524	46.60604	68.49467	17.30534
61.96707	49.63369	8.369427	54.37901
28.9013	20.58473	15.58098	60.54347
52.05759	35.05463	42.73849	41.27033
50.60503	54.25425	64.52019	23.08661
56.78954	47.49495	11.34584	6.163854
2.251747	21.84793	54.51714	30.57219
39.44349	52.53212	13.18604	29.91498
40.79134	6.021271	48.14325	58.69213
20.77187	71.46217	25.71548	56.11673
50.56493	40.35691	8.810541	24.7174
23.3896	56.12342	61.39897	5.450941
30.27143	43.4915	71.39979	70.67351
25.29218	28.32875	41.38618	8.670186
51.05506	17.87121	18.974	16.11789
68.49913	45.93991	43.32441	28.17725
4.693472	2.131443	9.668264	24.55031
11.82482	68.55483	47.26548	36.2599
17.95587	69.09842	71.66713	74.44749
22.78585	14.81906	55.73354	19.93866
73.03726	4.417219	45.30497	59.92413
56.59795	11.38371	3.88699	31.4366
2.14481	52.81506	45.32948	10.02026
74.33164	30.45189	43.83236	65.27543
2.222785	30.96207	56.2504	61.61284
51.18427	10.98492	35.03903	53.99805
63.76717	18.99628	47.82244	39.93808
66.87503	25.50829	65.897	55.5219
65.7767	2.634938	26.67122	33.77139

Answer 1

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

The Excel output is:

	R²	0.026
	Adjusted R²	0.000
	R	0.162
	Std. Error	28.826
	n	42
	k	3
	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	854.3926	3	284.7975	0.34	.7945
Residual	31,575.9299	38	830.9455
Total	32,430.3225	41
Regression output				confidence interval
variables	coefficients	std. error	t (df=38)	p-value	95% lower	95% upper
Intercept	62.0474
X1	-0.1610	0.1830	-0.880	.3846	-0.5314	0.2095
X2	-0.0973	0.1892	-0.514	.6099	-0.4803	0.2856
X3	0.0764	0.1639	0.466	.6440	-0.2555	0.4083

	r²	0.002
	r	-0.049
	Std. Error	28.440
	n	42
	k	1
	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	77.0951	1	77.0951	0.10	.7591
Residual	32,353.2274	40	808.8307
Total	32,430.3225	41
Regression output				confidence interval
variables	coefficients	std. error	t (df=40)	p-value	95% lower	95% upper
Intercept	56.0864
X2	-0.0560	0.1814	-0.309	.7591	-0.4227	0.3106

	r²	0.015
	r	-0.121
	Std. Error	28.265
	n	42
	k	1
	Dep. Var.	Y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	473.7874	1	473.7874	0.59	.4458
Residual	31,956.5350	40	798.9134
Total	32,430.3225	41
Regression output				confidence interval
variables	coefficients	std. error	t (df=40)	p-value	95% lower	95% upper
Intercept	59.3685
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