Analysis of Variance Source Regression Error Total D F MS 20 2 20 40 25 140 Pred

Question

Analysis of Variance Source Regression Error Total D F MS 20 2 20 40 25 140 Predictor Constant X1 X2 X3 X4 XS Coef 3.00 4.00 3.00 0.20 -2.5O 3.00 Stdev 1.50 3.00 0.20 O.O5 1.00 4.00 t-ratio 2.00 1.33 15.OO 4.OO -2.5O 0.7S 1. What is the sample size? 2. Compute the value of R square 3. Compute the multiple standard error of estimate 4. Conduct a global test of hypothesis to determine whether any of the regression coefficients are significant. Use the 0.05 significance level. 5. Test the regression coefficients individually or if we are going to take out any variable which one would that be? Use the 0.05 significance level.

Explanation / Answer

1. The abiove table shows error DF as 20 which is equal to n-k-1 where n is number of rows and k is number of explanatory variables. here k=5 as there are 5 predictors from x1 to x5. so n-5-1=20. So, n=26 which is the sample size

2.R square is = Sum of Squares of Regression /Totla Sum of Square =100/140=71.4%

3.Standard Error od Estimate is sqrt(Residual SS/n-k-1) = sqrt(40/(26-5-1))=1.4

4.p value for x1=0.2 arrived by using tdist(x,degrees of freedom, 2 tailed) where x is t ratio given in teh output. This is non significant. Degrees of Freedom is

p value for x2=1.0759*10^-12 which is <<<<0.05 hence significant

pvalue for x 3=0.0006 hence significant as p value <0.05

pvalue for x 4= 0.02 which is <0.05 hence significant

pvalue for x5= 0.46 not significant

5. The regresssion variable that need to be taken out are x5 and x1

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