1) Complete the following problem: The model Y = 0 + 1 X 1 + 2 X 2 + is tted to

Question

1) Complete the following problem:

The model Y = 0 + 1X1 + 2X2 + is tted to a data set with 10 observations.

(a) Supply values for the missing entries in the following ANOVA table.

Table 1: ANOVA Table

(b) Is the overall regression signicant (Hint: Use R to obtain the critical value of F)?

(c) What proportion of the variance of Y is explained by the regression model?

(d) Another model Y = 0 +1X1 + is tted to the same data set. Supply values for the missing entries in the following ANOVA table and use the extra sum of squares principle to test if variable X2 is important. State your hypothesis.

Source SS df MS F Regression 20 Error Total 34

Explanation / Answer

Solution-

After doing necessary calculatiosn we find the following table-

F statistic = 20 and critical value is given by - F2,7,0.05= 1.737

Since F statistic is greater than critical value, hence null hypothesis - model is not significant is rejected.

Hence model is significant.

proportion of the variance of Y is explained by the regression model is given by R2 =

SSG/SSE

= 14/20

= 0.7

Answers

TY!

Source SS df MS F Regression 20 2 = 20/2 = 10 = 10/(1/2) =20 Error = 34 - 20 = 14 10-3 = 7 = 7/14 = 1/2 Total 34 9

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