Project #16634 - statistic

Q1. At the second step of stepwise regression procedure the least squares prediction equation comes out to 

       be: _when variable X2 is entered in he model. A sample of 19 observations 

       gave SSX1=225.0, coefficient of correlation between X1 and X2 =-0.8 and SSE=81.0 when both X1 and 

      X2 are in the model. Choosing α=0.01, the following will be true.

X1 should stay in the model.     

X1 should not stay in the model.


Both a and c are true

















Q2. For a given sample size n=25, a least square linear prediction equation gave coefficient of determination R2 = 0.6 when 8 independent variables were in the model where as R2=0.5 when 7 independent are in the model. Using =0.01, the following is true.

a. Both adjusted R2 and R2 support the prediction equation with 8 independent variables.   

b. Adjusted R2  > R2  when 8 independent variables are in the model.

c.  Adjusted R2supports the inclusion of 8th variable but R2 does not support to use prediction equation

d. None of the above












Q3. In a mutilated record of multiple linear regression analysis, available legible statistics 

         are: n=41, SST = 201, SSE=21.00 and MSE=1.75. 

         The F-test for H0 for all βs equal to zero against not all are zero will support the following.

        a. H0 will be accepted

        b. F=t2 when H0 is true

         c. calculated F is less than 1.

        d. H1 will be accepted












Q4. An analyst selected a random sample of 20 cars to study the effect of weight of the car (X1) and horse 

       power of the car’s engine  (X2) on gasoline mileage (Y) as measured by miles/gallon, She computed 

       SSX1=140.0, SSX2=35.0, coefficient of correlation between X1 and X2=-0.095, SST=280, and got the 

       multiple linear regression equation: _Given that =0.05, the following is 

       true to test hypothesis  H0: _1  = 0 against H1: _1 ≠ 0

H0 will be accepted.

Calculated F will be close to 5.67

Calculated t will be close to 2.38

H1 will be accepted













Q5. 40 observations of a time series exhibiting linear trend and no seasonal effect are used to compute 

         least squares SSE=20 and  the value of Durbin-Watson  statistic D=0.9. While making decision about 

         the existence of first order autocorrelation it was found that two central  residuals in the 

         sequence –0.45, 1.2 and 1.3 and 2.2 with one time period lag were incorrectly used in place of 

         corresponding correct  residue values –0.45,  –2.1,  3.1 and 2.2. 

         The value of Durbin-Watson statistic indicates that there is

         a. Positive autocorrelation exists     

          b. No autocorrelation       

          c. Negative autocorrelation 

          d. No conclusion about autocorrelation 



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Due By (Pacific Time) 11/11/2013 8 pm
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