Run an excel data analysis for regression
A) What is the F test and interpret it
B) Run a T Test and interpret it
C) Use the hypothesis equation to see if you if you accept or reject the hypothesis
A) Using Excel:
SUMMARY OUTPUT | ||||||
Regression Statistics | ||||||
Multiple R | 0.992398792 | |||||
R Square | 0.984855361 | |||||
Adjusted R Square | 0.977283042 | |||||
Standard Error | 1.249867779 | |||||
Observations | 10 | |||||
ANOVA | ||||||
df | SS | MS | F | Significance F | ||
Regression | 3 | 609.5269832 | 203.1756611 | 130.0599363 | 7.55516E-06 | |
Residual | 6 | 9.373016791 | 1.562169465 | |||
Total | 9 | 618.9 | ||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
Intercept | -10.17024332 | 3.473128593 | -2.928265696 | 0.026346428 | -18.66868281 | -1.671803818 |
X1 | 0.027038115 | 0.012040996 | 2.245504802 | 0.065846812 | -0.002425142 | 0.056501372 |
X2 | 0.097052345 | 0.030147122 | 3.219290578 | 0.018153389 | 0.023284996 | 0.170819694 |
X3 | 0.524675168 | 0.059158249 | 8.869011174 | 0.000114333 | 0.379920149 | 0.669430187 |
F test:
The test statistic: F= 130. 0599
P-value= 0.000007
The test statistic is significant and rejects H0. There is enough evidence to support the claim that there is significant relationship with output variable.
B) T- test and interpret:
Coefficients | Standard Error | t Stat | P-value | |
Intercept | -10.17024332 | 3.473128593 | -2.928265696 | 0.026346428 |
X1 | 0.027038115 | 0.012040996 | 2.245504802 | 0.065846812 |
X2 | 0.097052345 | 0.030147122 | 3.219290578 | 0.018153389 |
X3 | 0.524675168 | 0.059158249 | 8.869011174 | 0.000114333 |
To interpret coefficients:
For every additonal unit of X1, output value increases by 0.027038115 unit
For every additional unit of X2, output value increases by 0.097052345 units
For every additonal unit of X3, output value increases by 0.524675168 units.
Hypothesis test:
The test statistic:
t(x1)= 2.2455 and P-value= 0.066
t(x2)= 3.2199 and p-value= 0.018
t(x3)= 8.8690 and p-value= 0.00014
C) Hypothesis tests:
The test statistic:
t(x1)= 2.2455 and P-value= 0.066
t(x2)= 3.2199 and p-value= 0.018
t(x3)= 8.8690 and p-value= 0.00014
At 0.05 significant level, X1 is not significant and X2, X3 are significant and good for prediciton.
X1- failed to reject H0
X2- Reject Ho
X3- Reject H0
Run an excel data analysis for regression A) What is the F test and interpret it...
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