Multiple Choice Questions

1. 
   smallest sum of squared residuals **
   
2. 
   largest sum of squared residuals
   
3. 
   smallest number of outliers
   
4. 
   largest number of points on the line
   
5. 
   none of the above
   

2. In a multiple regression analysis, there are 25 data points and 5 independent variables, and the sum of the squared differences between observed and predicted values of y is 160. The regression standard error will be:

1. 
   2.530
   
2. 
   3.464
   
3. 
   2.902**
   
4. 
   5.657
   
5. 
   none of the above
   

3. In a simple linear regression analysis, the following sum of squares are produced:

1. 
   20%
   
2. 
   80%**
   
3. 
   25%
   
4. 
   50%
   
5. 
   none of the above
   

1. 
   the relationship between x and y is positive
   
2. 
   the relationship between x and y is negative**
   
3. 
   as x increases, so does y
   
4. 
   as x decreases, so does y
   
5. 
   there is no relationship between x and y
   

5. A multiple regression equation includes 6 independent variables, and the coefficient of multiple determination is 0.91. The percentage of the variation in y that is explained by the regression equation is:

1. 
   91%**
   
2. 
   95%
   
3. 
   83%
   
4. 
   about 15%
   
5. 
   none of the above
   

6. A “fan” shape in a scatterplot indicates:

1. 
   unequal variance**
   
2. 
   a nonlinear relationship
   
3. 
   he absence of outliers
   
4. 
   sampling error
   

7. The values of the regression parameters _i are not known. We estimate them from the data.

a) True ** b) false c) Not enough information
8. Residual plots can be used to check the aptness of the model for the data.

a) True** b) False c) Not enough information

9. 
   We need to estimate the variance of the error terms because:
   

1. 
   It gives an indication of the variability of the distribution of y.
   
2. 
   It is needed for making inference concerning regression function and the prediction of y.
   

b) Only (II) is true.

3. 
   Both (I) and (II) are true.**
   
4. 
   Neither (I) nor (II) is true.