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Why is the random error term ? added to a multiple regression model?

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Calculate the upper and lower control limits for the x-chart.

In order to compare the means of two populations, independent random samples of 144 observations are selected from each population with the following results.
 
Sample 1 Sample 2
x1 = 7,123 x2 = 6,957
s1 = 175 s2 = 225
 
Use a 95% confidence interval to estimate the difference between the population means (?1 – ?2). ). Interpret the confidence interval.

3. Why is the random error term ? added to a multiple regression model?

6. In a study of feeding behavior, zoologists recorded the number of grunts of a warthog feeding by a lake in the 15 minute period following the addition of food. The data showing the number of grunts and and the age of the warthog (in days) are listed below:
       
       
       
Number of Grunts Age(days)  
82 117      
60 133      
31 147      
36 152      
55 159      
32 166      
54 175      
9 181      
12 187      
       
Find and interpret the value of r2.

8. In order to compare the means of two populations, independent random samples of 225 observations are selected from each population with the following results.
   
   
   
Sample 1 Sample 2
x1 = 478 x2 = 481
s1 = 14.2 s2 = 11.2
   
Test the null hypothesis H0: (?1 – ?2) = 0 against the alternative hypothesis Ha: (?1 – ?2) ? 0 using ? = .10. Give the significance level, and interpret the result.

Test the null hypothesis of independence of the two classifications, A and B, of the 3 × 3 contingency table shown below. Test using a = .01.
   
   
   
A B  
B1 B2 B3  
A1 19 40 60
A2 55 23 22
A3 31 42 47

A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let ?1 be the true mean weight of individuals before starting the diet and let ?2 be the true mean weight of individuals after 3 weeks on the diet.
   
   
   
Person Weight Before Diet Weight After Diet
1 156 149  
2 201 196  
3 194 191  
4 203 197  
5 210 206  
   
Summary information is as follows: d = 5, sd = 1.58. Test to determine if the diet is effective at reducing weight. Use a = .10.
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