Question

a) Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
10.7	81.6
13.7	81.5
36.7	56.5
4	72.1
50.7	23.2
47.6	-4.8
37.3	31.9
24.3	75.2
21.5	59.3
17.2	54.6
23.6	75.5
22.2	60.8
29.3	51
14	63.4
0.2	102.7
30.7	48.2
10.3	74.8
26.5	48.2
23.1	87

Verify that the correlation is significant at an ?=0.05?=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 39 on the response variable.

What is the predicted explanatory value?
x = _____

b) Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
83.5	16
61.9	69.3
89.1	36
75.7	51.3
76.6	43.4
94.5	38.8
47.2	102.4
66	75
83.2	-3.5
83.2	39
71.7	96.7
81.6	60.7
63.4	55.4
94.7	-61.1
56.8	138.1
90.2	-4.4
77.9	65.7
58	109.1

Verify that the correlation is significant at an ?=0.05?=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of -35.1 on the response variable.

What is the predicted explanatory value?
x =_____

c) Run a regression analysis on the following bivariate set of data with y as the response variable.

x	y
50.7	11.1
23.8	30.7
48.5	-3.6
19.5	34.7
12.1	48.3
31.8	21.7
47.6	16.3
25.7	39
20.6	43.4
46.8	8.5
51.1	16.5
33.8	17.9

Verify that the correlation is significant at an ?=0.05?=0.05. If the correlation is indeed significant, predict what value (on average) for the explanatory variable will give you a value of 23.4 on the response variable.

What is the predicted explanatory value?
x =_____

Answer 1

(a)

Following is the output of regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.843323289
R Square	0.711194169
Adjusted R Square	0.694205591
Standard Error	13.71605863
Observations	19
ANOVA
	df	SS	MS	F	Significance F
Regression	1	7875.711824	7875.711824	41.86307746	5.76252E-06
Residual	17	3198.214492	188.1302642
Total	18	11073.92632
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	96.35851315	6.421290985	15.00609665	3.07625E-11	82.81077352	109.9062528
x	-1.551198715	0.239746271	-6.470168272	5.76252E-06	-2.057019127	-1.045378302

The correlation coeffcient is: 0.8433

The p-value of slope is : 0.0000

Since p-value of slope is linear regression is same as t-test for correlation coeffcient so p-value of correlation coeffcient is 0.000.

Since p-value is less than 0.05 so correlation coefficient is significant.

The linear equation is:

y' = 96.359-1.551x

For y'=39 we have

39 = 96.359-1.551x

x = 36.982