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1. The test statistic corresponding to the intercept of the regression line is 1

ID: 3217813 • Letter: 1

Question

1. The test statistic corresponding to the intercept of the regression line is 1.291.

2. The correlation coefficient between X and Y is 0.758.

SUMMARY OUTPUT Regression Statistics Multiple R 0.758 R Square 0.575 0.433 Adjusted R Square 1.191 Standard Error Observations ANOVA df SS MS F Signifi F ficance 0.138 Regression 5.746 5.746 4.052 4.254 1.418 Residual Total 10 Coefficients Standard Error t Stat P-value Lower 95% er 95% 1.002 1 0.287 1.291 1.293 1.895 4.480 Intercept 0.164 -0.095 0.424 0.082 2.013 0.138

Explanation / Answer

here Y is dependent variable and X is indpendent variable. Fitted regression equation Y=a+bx is given as

Y=1.292+0.164X

(1) The test statistic t corresponding to the intercept of the regression line is 1.291, which is calculated as

t=coefficient/SE(coefficient)=1.293/1.002=1.291,

its p-value=0.287 is more than alpha=0.05, so we fail to reject null hypothesis H0:intercept a=0

(2) here coefficient of determination R square=0.575 ,

for simple linear regression R-square is the square of correlation coefficient

the correlation coefficient between X and Y in this case=sqrt(R-square)=sqrt(0.575)=0.758