\(\hat{A} = 8.15 + 0.6X_{1} + 0.54X_{2}\)

Here , Total sum of square = 1493, and Sum of square due to error = 91

Find i) R2 and interpret it. ii) Test the overall significance of model

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Login NowTSS = 1493

SSE = 91

SSR = TSS – SSE = 1493 – 91 = 1402

MSE = SSE / k = 1402 / 2 = 701

MSE = SSE / n-k-1 = 91/7-2-1 = 22.75

R^{2} = SSR / TSS = 1402 / 1493 = 0.939 = 93.9%

It means 93.9% variation in y is explained by x_{1} and x_{2}

To test overall significance of regression model

Let β_{1} and β_{2} be population regression coefficients of Y on X_{1} keeping X_{2} constant and population regression coefficient of Y on X_{2} keeping X_{1} constant.

**Problem to test**

H_{0} : β_{1} = β_{2} = 0

H_{1} : At least one β_{1} is different from zero, i = 1,2

**Test Statistic**

F = \(\frac{MSR}{MSE}\) = \(\frac{701}{22.75}\) = 30.81

**Critical Value**

At α = 0.05 level of significance, critical value is F_{α}_{(k, n-k-1)} =6.944

**Decision**

F = 30.81 > F_{tabulated} = 6.944, reject H_{0} at 5% level of significance

**Conclusion**

There is linear relationship of dependent variable y with at least one of the independent variable x^{‘}s

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## Discussion