Problems E270 HW 7

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 Given are five observations for two variables, x and y.     
  xy       
  13       
  28       
  36       
  411       
  516       
           
1The predicted value of y when x = 4 is:      
a 9.6        
b 10.6        
c 11.7        
d 12.2        
           
2The standard error of estimate for the model is:     
a2.214         
b2.033         
c1.949         
d1.822         
           
3The percent of variations in y explained by the variations in x is:    
a59.4%         
b68.1%         
c76.2%         
d85.1%         
           
Next FOUR questions are based on the following      
How much does education affect wage rates?  Use the following data to develop an estimated regression equation that could be used to predict the WAGE for a given number of years of education. 
 
 yx        
 WAGEEDUC        
 18.7016        
 11.5012        
 15.0416        
 25.9514        
 24.0312        
 20.0012        
 53.8416        
 25.0012        
 28.8516        
 16.8313        
 14.8012        
 43.2516        
 19.2312        
 14.0014        
 8.0012        
 57.7021        
 20.0012        
 20.8318        
 22.0011        
 68.7514        
 10.5012        
 9.8813        
 10.9612        
 8.2513        
 14.8618        
           
           
4The numerator of the formula to compute the slope coefficient of the regression equation is ________. 
 Use Excel!!        
a360.33         
b460.33         
c560.33         
d660.33         
           
5The estimated regression equation predicts that the expected wage rate for a person with 16 years of education is ______. 
  
a$29.45         
b$27.45         
c$25.45         
d$23.45         
           
6In the sample, the observed wage data deviate from the predicted wage, on average, by $ ________. 
a12.35         
b13.35         
c14.35         
d15.35         
           
7What proportion of the variations in wage can be explained by education?   
a0.1862         
b0.2262         
c0.3462         
d0.4562         
           
8The standard error of the slope coefficient is ______.     
a3.1606         
b2.1606         
c1.1606         
d0.9606         
           
9The 95% confidence interval for the population slope parameter is:    
a1.814.21        
b1.414.61        
c1.015.01        
d0.615.41        
           
10To test, at a 5% level of significance, the hypothesis H₀: β₁ = 0 versus H₁: β₁ ≠ 0, the t test statistic is 

|t| = ______.		 
  
a2.593Reject the null hypothesis.      
b2.935Reject the null hypothesis.      
c3.277Reject the null hypothesis.      
d3.619Reject the null hypothesis.      
           
Next TEN questions are based on the computer output below relating to the following problem  
A regression model relating y, the annual sales (in thousands of dollars) at a branch office to x, number of salespersons at the office, provided the following regression summary output. 
 
           
The exercise involves filling in the values for the numbered cells in yellow.    
           
 SUMMARY OUTPUT         
 Regression Statistics        
 Multiple R         
 R Square (5)       
 Adjusted R Square        
 Standard Error(4)       
 Observations(3)       
           
 ANOVA         
  dfSSMSFSignificance F    
 Regression1(2) 61.6661.38E-05    
 Residual28(1)82.1      
 Total299127.4       
           
  CoefficientsStd Errort StatP-valueLower 95%Upper 95%   
 Intercept80.24611.3337.0811.06E-0757.031103.461   
 PERSONS50.386(6)(7)5.99E-10(8)(9)   
           
           
11How many branch offices were involved in the study?     
a29         
b30         
c31         
d32         
           
12The predicted annual sales at an office with 12 salespersons is $______ thousand.   
a$714.88         
b$704.88         
c$694.88         
d$684.88         
           
13The value for SSE in (1) is:       
a2198.8         
b2298.8         
c2398.8         
d2498.8         
           
14The variance of the prediction error is ______      
a2298.8         
b47.95         
c82.1         
d9.06         
           
15The value for SSR in (2) is:       
a6828.6         
b6928.6         
c7028.6         
d7128.6         
           
16The value for the standard error of estimate se(e) in (4) is:    
a9.303         
b9.061         
c8.819         
d8.577         
           
17The value for R² in (5) is:       
a0.8513         
b0.8169         
c0.7825         
d0.7481         
           
18Given ∑(x − x̅)² = 2.732, the value of the standard error of the slope coefficient in (6) is:  
a6.013         
b5.482         
c4.951         
d4.420         
           
19The value of the t stat |t| in (7) is:       
a10.876         
b9.191         
c7.506         
d5.821         
           
20The lower and upper end of a 95% confidence interval for the population slope parameter β₁ in (8) and (9), respectively, are: 
  
a34.43266.340        
b36.00164.771        
c39.15961.613        
d42.15058.622        
     
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