Is there a direct or indirect relationship between the dista

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

How much damage would you estimate (in dollars) for a fire 9 miles from the nearest fire station?(Round your answer to the nearest dollar amount. Omit the \"$\" sign in your response.)

Determine the coefficient of determination. (Round your answer to 4 decimal places.)

Coefficient of determination:

Fill in the blank below. (Round your answer to 4 decimal place. Omit the \"%\" sign in your response.)

State the decision rule for .01 significance level: H₀ : ? = 0; H₁ : ? ? 0. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Is there any significant relationship between the distance from the fire station and the amount of damage? Use the .01 significance level.

(a-1)

Write out the regression equation. (Round your answers to 4 decimal places.)

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 Regression 1,815.5782 1 1,815.5782 40.82 Residual 1,245.4934 28 44.4819 Total df MS 3,061.0716 29 Regression output Variables Coefficients Std. Error t(df-28) Intercept Distance- 3.556 6.39 13.3334 3.0617 9.032

Solution

(a-1)

Write out the regression equation. (Round your answers to 4 decimal places.)

  Y = 13.3334 + 4.7711 X.

(a-

2Is 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 (Click to select)direct

(b)

How much damage would you estimate (in dollars) for a fire 9 miles from the nearest fire station?(Round your answer to the nearest dollar amount. Omit the \"$\" sign in your response.)

  Y = 13.3334 + 4.7711*9 =56.2733

Answer = 56

(c-1)

Determine the coefficient of determination. (Round your answer to 4 decimal places.)

Coefficient of determination:   1815.5782/3061.0716= 0.5931

(c-2)

Fill in the blank below. (Round your answer to 4 decimal place. Omit the \"%\" sign in your response.)

59.3119 % of the variation in damage is explained by variation in distance.

(d-1)

Determine the coefficient of correlation. (Round your answer to 4 decimal places.)

  Coefficient of correlation: 0.7701

(d-2)

Choose the right option.

There is a fairly solid direct link between the variables.

(d-3)

How did you determine the sign of the correlation coefficient?

  It is (Click to select)positive because the slope is (Click to select)positive.

(e-1)

State the decision rule for .01 significance level: H₀ : ? = 0; H₁ : ? ? 0. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

  Reject H₀ if t < -2.763 or   t > 2.763

(e-2)

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

  Value of the test statistic: 6.39

(e-3)

Is there any significant relationship between the distance from the fire station and the amount of damage? Use the .01 significance level.

(Click to select)Reject H₀. There is (Click to select)significant relationship between distance and fire damage.

(a-1)

Write out the regression equation. (Round your answers to 4 decimal places.)