question archive The following regression output was obtained from a study of architectural firms
The following regression output was obtained from a study of architectural firms
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The following regression output was obtained from a study of architectural firms. The dependent variable is the total amount of fees in millions of dollars. Predictor Coeff SE Coeff t p-value Constant 7.987 2.967 2.690 0.010 X1 0.122 0.031 3.920 0.000 X2 –1.120 0.053 –2.270 0.028 X3 –0.063 0.039 –1.610 0.114 X4 0.523 0.142 3.690 0.001 X5 –0.065 0.040 –1.620 0.112 ________________________________________ Analysis of Variance Source DF SS MS F p-value Regression 5 3710.00 742.00 12.89 0.000 Residual Error 46 2647.38 57.55 Total 51 6357.38 ________________________________________ X1 is the number of architects employed by the company.X2 is the number of engineers employed by the company.X3 is the number of years involved with health care projects.X4 is the number of states in which the firm operates.X5 is the percent of the firm’s work that is health care–related. a. Write out the regression equation. (Round your answers to 3 decimal places. Negative answers should be indicated by a minus sign.) ? = + X1 + X2 + X3 + X4 + X5. b. How large is the sample? How many independent variables are there? Sample n Independent variables k ________________________________________ c-1. State the decision rule for .05 significance level: H0: ?1 = ?2 = ?3 =?4 =?5 =0; H1: Not all ?’s are 0.(Round your answer to 2 decimal places.) Reject H0 if F > c-2. Compute the value of the F statistic. (Round your answer to 2 decimal places.) Computed value of F is c-3. Can we conclude that the set of regression coefficients could be different from 0? Use the .05 significance level. H0. of the regression coefficients are zero. For X1 For X2 For X3 For X4 For X5H0: ?1 = 0 H0: ?2 = 0 H0: ?3 = 0 H0: ?4 = 0 H0: ?5 = 0H1: ?1 ? 0 H1: ?2 ? 0 H1: ?3 ? 0 H1: ?4 ? 0 H1: ?5 ? 0________________________________________ d-1. State the decision rule for .05 significance level. (Round your answers to 3 decimal places.) Reject H0 if t < or="" t=""> . d-2. Compute the value of the test statistic. (Round your answers to 2 decimal places. Negative answers should be indicated by a minus sign.) t ? value X1 X2 X3 X4 X5 ________________________________________ d-3. Which variable would you consider eliminating? Consider eliminating variables .
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Rajeevan Pillai :
The regression equation is
7.987 + 0.12242 X1 – 0.12166 X2 – 0.06281 X3 + 0.5125 X4 -0.06472 X5
Rajeevan Pillai :
The sample size is 52
Rajeevan Pillai :
There are 5 independent variables.
Rajeevan Pillai :
X1, X2, X3, X4 and X5.
Rajeevan Pillai :
F = 12.89
Degrees of freedom 5 and 46
Critical value is 2.417356
All coefficients are not equal to zero
JACUSTOMER-61rcw5i5- :
Are you able to do c, d, and e. Conduct a global test and test of hypothesis.
Rajeevan Pillai :
Individual variables
Critical value of t with 46 df is 2.0129
The t values for the variables are
X1 3.92
X2 -2.27
X3 -1.61 not significant
X4 3.69
X5 -1.62 not signifiacant
X3 and X5 can be eliminated.
Rajeevan Pillai :
Global test says that all coefficients are not equal to zero.
Rajeevan Pillai :
some variable is different from zero
Rajeevan Pillai :
Test for individual variables says that the coefficients of X3 and X5 are not significantly different from zero. So they can be deleted.
Rajeevan Pillai :
The strategy for deleting variables is
Rajeevan Pillai :
first delete the least significant variable. In this case it is X3
Rajeevan Pillai :
Then X5.
