Question

1. Questions 16-23

   
   A multiple linear regression was used to study how family spending ( y) is influenced by income ( x ₁), family size ( x ₂), and additions to savings ( x₃). The variables y, x ₁, and x ₃ are measured in thousands of dollars per year. The following results were obtained.
   

   ANOVA
   	DF	SS
   Regression		42.450
   Residual	11	2.141
   Total

   	Coefficients	Standard Error
   Intercept	0.012
   x 1	0.742	0.071
   x 2	0.201	0.186
   x 3	-0.540	0.890

     
   16.  What was the number of families used in this study?

   	a.	15
   	b.	11
   	c.	14
   	d.	12
   	e.	None of the above

2 points   

QUESTION 17

1. Q17:  The value of the F statistic for testing the overall significance of the regression model is

   	a.	9.75
   	b.	72.70
   	c.	50.40
   	d.	42.45
   	e.	None of the above

2 points   

QUESTION 18

1. Q18:  The p-value for testing the overall significance of the regression model is

   	a.	Less than 0.01
   	b.	Between 0.01 and 0.025
   	c.	Between 0.025 and 0.05
   	d.	More than 0.05
   	e.	None of the above

2 points   

QUESTION 19

1. Q19:  The percent of variations in family spending explained by family income, size and additions to savings is

   	a.	95.2%
   	b.	90.3%
   	c.	85.2%
   	d.	85.9%
   	e.	None of the above

2 points   

QUESTION 20

1. Q20:  At 5% significance level, the conclusion is that the

   	a.	Model is insignificant
   	b.	Model is significant
   	c.	X1 is insignificant
   	d.	X3 is significant
   	e.	None of the above

2 points   

QUESTION 21

1. Q21:  The value of the t statistic for testing whether the family spending and addition to savings are related is

   	a.	1.27
   	b.	-0.59
   	c.	-0.69
   	d.	-0.61
   	e.	None of the above

2 points   

QUESTION 22

1. Q22:  The (positive) critical t value for testing whether the family spending and addition to saving are related at a 5% significance level is

   	a.	0.846
   	b.	2.145
   	c.	1.796
   	d.	2.201
   	e.	None of the above

2 points   

QUESTION 23

1. Q23: The 95% confidence interval for the parameter β ₃ extends from

   	a.	1.328 to 3.372
   	b.	-0.649 to 1.651
   	c.	-2.449 to 1.369
   	d.	-2.499 to 1.419
   	e.	None of the above

Answer all questions

Answer 1

ANOVA
	DF	SS	MS	F
Regression	3	42.45	14.15	72.70
Residual	11	2.141	0.19
Total	14

16 ) answer: 14+1 = 15

17) F=72.70

18)
a.  
Less than 0.01

19) R²=SSR/SST=0.952 or 95.2%

20) Model is significant

21) test stat=-0.54/0.89 = -0.61

22) =T.INV.2T(0.05,11) = 2.201

23)

confidence interval for slope                  
                  

alpha,α =    0.05              
estimated slope=   -0.54              
std error =    0.89              
                  

t critical value =    1.9600   [excel function: =t.inv.2t(α,df) ]          
                  
margin of error ,E = t*std error =    1.9600   *   0.89   =   1.74440
                  
95%   confidence interval is ß1 ± E               
lower bound = estimated slope - margin of error =    -0.54   -   1.7444   =   -2.2844
upper bound = estimated slope + margin of error =    -0.54   +   1.7444   =   1.2044

1. None of the above