Both parts please, show work a) Run a regression analysis on the following bivar

Question

Both parts please, show work

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 109.5 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 23.4 on the response variable.

What is the predicted explanatory value?
x = _____

x y 49.3 65.5 34.7 103.1 60.4 50.5 43.6 78.9 23.5 109.8 40.9 71.3 38.9 60.6 31.3 96.6 43 97.2 41.9 68.2 40.4 79.7

Explanation / Answer

(a) the regression equation is given as y=146.02 - 1.62*x

for y=109.5,x=(109.5-146.02)/(-1.62)=22.54

the correlation between x and y =corr(x,y)=r=-0.8021 ,

we use t-test and

t =r/sqrt[(1—r2)/(n—2)]=(-0.8021)/SQRT((1-(-0.8021)*(-0.8021))/(11-2))=-4.03 with n-2=11-2=9 df

critical t(0.05,9)=2.26 is less than absolute value of calcuated t=4.03, so correlation coefficeitn is significant ( from zero)

following information has been generated using ms-excel

(b) the regression equation y=58.73-x

for y=23.4, x=58.73-23.4=25.33

the correlation between x and y =corr(x,y)=r=-0.9109,

we use t-test and

t =r/sqrt[(1—r2)/(n—2)]=(-0.9109)/SQRT((1-(-0.9109)*(-0.9109))/(11-2))=-6.62 with n-2=11-2=9 df

critical t(0.05,9)=2.26 is less than absolute value of calcuated t=6.62, so correlation coefficeitn is significant ( from zero)

following information has been generated using ms-excel

SUMMARY OUTPUT Regression Statistics Multiple R 0.802120041 R Square 0.64339656 Adjusted R Square 0.603773955 Standard Error 12.05217637 Observations 11 ANOVA df SS MS F Significance F Regression 1 2358.667221 2358.667 16.23812 0.002974517 Residual 9 1307.294597 145.255 Total 10 3665.961818 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 146.0170506 16.75014691 8.717359 1.11E-05 108.1255859 183.9085153 X Variable 1 -1.618190571 0.401570507 -4.02965 0.002975 -2.526606168 -0.709774974

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