a) Run a regression analysis on the following bivariate set of data with y as th

Question

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

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.

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.

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 =_____

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

Explanation / Answer

(a)

Following is the output of regression analysis:

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

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

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