Suppose that a sample data set containing 30 observations results in the estimat

Question

Suppose that a sample data set containing 30 observations results in the estimated linear regression equation y = 16.67 - 0.4x_1 + 0.13x_2. Suppose also that SSE = 392.985 and SSR = 804.742. Conduct an F-test at the 0.05 significance level to determine if the equation represents a statistically significant model of the relationship among x_1, x_2 and y based on this sample of observations. H_0: H_a: alpha = Test Statistic (here): Rejection decision (Explain): Conclusion (Interpret the rejection decision in context):

Explanation / Answer

H0: The equation is not statistically significant model of the relation between x1 , x2 and y

H1: The equation is statistically significant model of the relation between x1 , x2 and y

alpha = 0.05

Test statistic :

Mean square Regression = 804.742 / 2 =402.371

Meas square Error = 392.985 / 27 = 14.555

Test statistic F = 402.371 / 14.555 = 27.6448

Decision

Critical value of F = 3.354

Here F value > F critical value, so we reject H0

Thus we conclude that the equation is statistically significant model of the relation between x1 , x2 and y

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