What should R2 be if all independent variables are able to fully explain y by our model?

statistics

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CALCULATION QUESTIONS

The following outputs were generated when Excel was used:

 SUMMARY OUTPUT Regression Statistics Multiple R 0.9019 R Square Adjusted R Square 0.7668 Standard Error 328.4111 Observations *1 ANOVA df SS MS F Significance F Regression *2 *4 1881222.0224 *7 0.0001 Residual *3 *5 *6 Total 15 6937912.0000 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -64.5812 985.2699 -0.0655 0.9488 -2211.2999 2082.1376 X Variable 1 27.4377 *8 4.0747 0.0015 810.0000 42.1093 X Variable 2 1.3093 1.8227 *9 0.4863 *10 *11 X Variable 3 1.1780 0.7831 1.5042 0.1584 *12 2.8842

a.       Complete the empty fields (with * - there are 12 of it) in the above table.

c.       What should R2 be if all independent variables are able to fully explain y by our model?

d.      Test whether y is related to any of the X’s (the overall significance of the model).  Use a significance level of 0.01.

1. Find the value of y if :

X1:73

X2: 300

X3: 250

Question

a.      What is the standard error of the multiple regression model when  k=4   n=100 SSExplained=200,  SSTotal=1720

b.      Explain briefly 3 assumptions of CLRM?

c.       Find the value of A in the following :

(i)        P ( Z > 100 ) = A

(ii)      P( t > B ) = 0 .98    assuming n=10

(iii)    P(t > 2.831) = C     assuming n=21

d.      Given E(X) = 7, E(Y) = 12, E(XY) = 48, Var(X) = 16,  Var(Y) =25,  and X and Y are independent events,  compute:

E(4X - 6Y)

Cov(5X,3Y)

Cov( X+2Y, 4X-2Y)

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