A multiple regression analysis resulted in the estimated regression equation y =

Question

A multiple regression analysis resulted in the estimated regression equation y = 8 - 3x_1 + 5x_2 -2x_3. What is the residual associated with the observation y = 0 when x_1 = 1, x_2 = 0, and x3 = -1? Suppose that a sample data set containing 30 observations results in the estimate 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: Ha: alpha =

Explanation / Answer

26) predicted value =yhat=8-3*1++5*0-2*(-1)=7

hence residual=actual value -predicted value =0-7=-7

Ho: all coefiificient are equal to 0. or model is insignificant (insignificant)

Ha: coeffiicient are not equal to 0 (model is siognificant)

alpha =0.05

here degree of freedom of regression = k-1 =3-1 =2

degree of freedom of residual =n-k =30-3=27

hence

test stat=27.64

rejection decision: as test stat is greater then critical value ; we reject null hypothesis.

conclusion: from above we have sufficient evidence to conclude that model is significant.

Source DF SS MS F P F crit regression 2 804.7420 402.371 27.64 0.0000 3.354131 Residual error 27 392.9850 14.555 Total 29 1197.7270

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