Question

Exercise 13-10 (LO13-2)

A study of 8 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.75.

1. State the decision rule for 0.010 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

     

reject H0 if t>

Exercise 13-20 (LO13-3)

The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.

Car				Age (years)				Selling Price ($000)
	1				11				12.1
	2				8				10.5
	3				14				5.7
	4				17				4.9
	5				9				5.0
	6				8				13.4
	7				10				10.5
	8				14				9.0
	9				13				9.0
	10				17				4.5
	11				6				12.5
	12				6				11.5

2. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)

For each additional year, the car decreases ______ in value.

Exercise 13-60 (LO13-2, LO13-3, LO13-5)

Waterbury Insurance Company wants to study the relationship between the amount of fire damage and the distance between the burning house and the nearest fire station. This information will be used in setting rates for insurance coverage. For a sample of 30 claims for the last year, the director of the actuarial department determined the distance from the fire station (x) and the amount of fire damage, in thousands of dollars (y). The MegaStat output is reported below.

ANOVA table
Source	SS	df	MS		F
Regression	1,870.5782	1	1,870.5782		41.23
Residual	1,270.4934	28	45.3748
Total	3,141.0716	29

Regression output
Variables	Coefficients	Std. Error	t(df=28)
Intercept	13.4867	3.1191	2.21
Distance–X	5.2717	0.8211	6.42

How much damage would you estimate for a fire 4 miles from the nearest fire station? (Round your answer to the nearest dollar amount.) [THE ANSWER IS NOT 35]

Estimated Damage

State the decision rule for 0.01 significance level: H₀ : ρ = 0; H₁ : ρ ≠ 0. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.)

reject H0 if t<

or t>

Answer 1

Exercise 13-10 (LO13-2)

A study of 8 worldwide financial institutions showed the correlation between their assets and pretax profit to be 0.75.

1. State the decision rule for 0.010 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

Solution:

n=   8  
alpha,α =    0.01  
correlation , r =   0.7500  
      
Df =    n-2 =   6
  
critical t-value =    3.1427 [excel formula =t.inv.rt(0.01,6) ]

reject H0 if t>

3.1427

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Exercise 13-20 (LO13-3)

The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price

excel output for regression is given below

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.73877
R Square	0.54578
Adjusted R Square	0.500359
Standard Error	2.29433
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	63.2505	63.2505	12.01579	0.006058
Residual	10	52.6395	5.26395
Total	11	115.89
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	15.87264	2.076681	7.643275	1.75E-05	11.24551	20.49977	11.24551	20.49977
age	-0.61558	0.177585	-3.46638	0.006058	-1.01126	-0.21989	-1.01126	-0.21989

so, predicted selling price($000)=15.8726 - 0.6157*age

2. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)

For each additional year, the car decreases $616 in value.