Apply SAS to the following data and answer questions. 1.) Report the analysis of

Question

Apply SAS to the following data and answer questions.

1.) Report the analysis of variance table and use the information shown in the output of the table to answer the following questions. Is the overall regression statistically significant (Using ? = 0.05)? What is the portion of the total variation about Y explained by X1 and X2?

2.)  Carry out the following model diagnostic by fitting data to a regression model with X1 or X2 alone. Answer the following questions.

How useful is the regression using X1 alone? Explain your answer and present the evidence.

How much contribution does X2 make to the regression, given that X1 is already in the regression? Explain your answer and present the evidence.

How useful is the regression using X2 alone? Explain your answer and give the evidence.

How much contribution does X1 make to the regression, given that X2 is already in the regression? Explain your answer and present the evidence. Make a summary of the above testing.

3.)What is the 90% confidence interval for ?1? Find the 90% confidence interval for E(y|x1 = 3, x2 = 5).

(please show me the sas code, especially for part2 question)

x1 1 4 9 11 3 8 5 10 2 7 6 x2 8 2 -8 -10 6 -6 0 -12 4 -2 -4 y 6 8 1 0 5 3 2 -4 10 -3 5 Y = B, + B1 X1 + B2 + e

Explanation / Answer

1) when y is regressed on x1 and x2

overall significance F = 0.0164 < 0.05

hence the overall model is significant

2) when X1 is only there ,R^2 = 0.61095

it means that 61.1 % of variation in y is explained by x1 alone

the model is significant as p-value = 0.004489 < 0.05

when we include x2 also , when x1 is already present

R^2 becomes 0.6421

that is 64.21 %

when x2 is only included

R^2 =0.517515

p-value = 0.01258 , hence x2 alone is significant

SUMMARY OUTPUT Regression Statistics Multiple R 0.801314709 R Square 0.642105263 Adjusted R Square 0.552631579 Standard Error 2.915475947 Observations 11 ANOVA df SS MS F Significance F Regression 2 122 61 7.176470588 0.0164067 Residual 8 68 8.5 Total 10 190 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 14 6.095003803 2.296963292 0.050710647 -0.055103974 28.0551 x1 -2 1.198437283 -1.668839938 0.133701723 -4.763601329 0.763601 x2 -0.5 0.599218641 -0.834419969 0.428255902 -1.881800665 0.881801

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