Question

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 | 1,835.5782 | 1 | 1,835.5782 | 40.45 | |

Residual | 1,270.4934 | 28 | 45.3748 | ||

Total | 3,106.0716 | 29 | |||

Regression output | |||

Variables | Coefficients | Std. Error | t(df=28) |

Intercept | 13.985 | 3.1125 | 2.34 |

Distance–X | 5.5828 | 0.8778 | 6.36 |

**a-1.** Write out the regression equation.
**(Round your answers to 3 decimal places.
**

Y= ............................... +...............................X.

**a-2.** Is there a direct or indirect relationship
between the distance from the fire station and the amount of fire
damage?

The relationship between distance and damage is ...................................

b )How much damage would you estimate for a fire 7 miles from
the nearest fire station? **(Round your answer to the nearest
dollar amount.)**

Estimated damage .......................

**c-1.** Determine and interpret the coefficient of
determination. **(Round your answer to 3 decimal
places.)**

Coefficient of determination..................................

**c-2.** Fill in the blank below. **(Round
your answer to one decimal place.)**

..................................... % of the variation in damage is explained by variation in distance.

**d-1.** Determine the correlation coefficient.
**(Round your answer to 3 decimal places.)**

Correlation Coffecient.................

**d-2.** Choose the right option.

There is a fairly solid....................................link between the variables.

**d-3.** How did you determine the sign of the
correlation coefficient?

ıt is ...................................because the slope is .........................

**e-1.** State the decision rule for 0.01
significance level: *H*_{0} : *ρ* = 0;
*H*_{1} : *ρ* ≠ 0. **(Negative value
should be indicated by a minus sign. Round your answers to 3
decimal places.)**

Reject H0 if t <..............................or t > ..............................

**e-2.** Compute the value of the test statistic.
**(Round your answer to 2 decimal places.)**

value of the test statistic.............................

**e-3.** Is there any significant relationship
between the distance from the fire station and the amount of
damage? Use the 0.01 significance level.

.....................H0.There is ......................................relationship between distance and fire damage.

Answer #2

**a-1.**

Y=13.985 + 5.5828 X.

**a-2.**

The relationship between distance and damage is
**direct** .

**b.**

Estimated damage is **Y=13.985 + 5.5828*7 =
53.0646**

**c-1.**

Coefficient of determination is **1835.5782/3106.0716 =
0.59096**

**c-2.**

**59.096 %** of the variation in damage is
explained by variation in distance.

**d-1.**

Correlation Coffecient is **0.7687**

**d-2.**

There is a fairly solid **direct** link between the
variables.

**d-3.**

ıt is **Positive** because the slope is
**Positive.**

**e-1.**

Using table of critical vaues for t-distribution we get critical values as -2.763 and 2.763.

Reject H0 if t **< -2.763** or t **>
2.763**

**e-2.**

value of the test statistic **6.36**

**e-3.**

**Reject Ho** There is
**significant**relationship between distance and fire
damage.

**Let me know in the comment section if anything is not
clear. I will reply ASAP!
If you liked the answer, please give a thumbs-up. This will be
quite encouraging for me.Thank-you!**

answered by: anonymous

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...

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...

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...

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...

The authors of a paper presented a correlation analysis to
investigate the relationship between maximal lactate level
x and muscular endurance y. The accompanying data
was read from a plot in the paper.
x
410
740
770
790
850
1035
1210
1240
1290
1390
1475
1480
1505
2200
y
3.80
3.90
4.80
5.30
3.90
3.40
6.40
6.88
7.55
4.95
7.90
4.45
6.50
8.90
Sxx = 2,619,073.214, Syy
= 39.4021, Sxy = 7632.018. A scatter plot shows
a linear pattern.
(a)...

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
9
8.1
2
7
6.0
3
11
3.6
4
12
4.0
5
8
5.0
6
7
10.0
7
8
7.6
8
11
8.0
9
10
8.0
10
12
6.0
11
6
8.6
12
6
8.0...

The owner of Maumee Motors 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 Maumee Motors during the last
year:
Car
Age (years)
Selling Price ($ thousands)
Car
Age (years)
Selling Price ($ thousands)
1
8
$9.5
7
6
$10.0
2
13
5.5
8
2
5.5
3
7
9.7
9
1
9.6
4
15
3.6
10
4
3.1
5
9
3.2
11...

What is the relationship between the amount of time statistics
students study per week and their final exam scores? The results of
the survey are shown below.
Time
9
3
13
5
15
8
5
16
Score
80
75
91
75
93
78
82
91
Find the correlation coefficient:
r=r= Round to 2 decimal places.
The null and alternative hypotheses for correlation are:
H0:H0: ? μ r ρ == 0
H1:H1: ? r ρ μ ≠≠ 0
The p-value is: (Round to four...

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