Solve the missing values in the following regression model. Write down all solutions along with their key letter.
Regression Statistics | ||||||||
Multiple R | 0.489538 | |||||||
R Square | 0.239648 | |||||||
Adjusted R Square | 0.231889 | |||||||
Standard Error | 11.76656 | |||||||
Observations | 100 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 4276.457 | 30.88765 | 2.35673E-07 | ||||
Residual | 138.452 | |||||||
Total | ||||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 99.0% | Upper 99.0% | |
Intercept | -24.1551 | 12.83013 | -1.88268 | 0.062709 | -49.61605579 | 1.305895 | -57.8589 | 9.548787 |
Food | 3.167042 | 0.569851 | 2.36E-07 | 2.03619109 | 4.297893 | 1.670083 | 4.664001 |
For simple linear regression model, the formula of degrees of freedom are as follows:
Degrees of freddom for residual = n - 2 = 100 - 2 = 98
(Where n = # of observations )
Degrees of freedom for total = n - 1 = 100 - 1 = 99
Formula of ME regression = ( SS_{reg} / df_{reg}) = 4276.457
Formula of ME residual= ( SS_{res} / df_{res})
THerefore SS_{res.} = MS_{res.} * df_{res.} = 138.452 * 98 = 13568.3
SS_{total} = SS_{reg.} + SS_{res.} = 4276.457 + 13568.3 = 17844.76
t Stat = Corresponding coefficient / SE(coefficient) = 3.167042/0.569851 =5.557667
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