Exercise 13-60 (Algo) (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 here: ANOVA table Source SS df MS F Regression 1,835.5782 1 1,835.5782 40.4537 Residual 1,270.4934 28 45.3748 Total 3,106.0716 29 Regression output Variables Coefficients Std. Error t(df=28) Intercept 14 3.1125 2.34 Distance–X 6 0.8778 6.36 Click here for the Excel Data File a-1. Determine the regression equation. (Round your answers to 3 decimal places.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Exercise 13-60 (Algo) (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 here:
| ANOVA table | ||||||
| Source | SS | df | MS | F | ||
| Regression | 1,835.5782 | 1 | 1,835.5782 | 40.4537 | ||
| Residual | 1,270.4934 | 28 | 45.3748 | |||
| Total | 3,106.0716 | 29 | ||||
| Regression output | |||
| Variables | Coefficients | Std. Error | t(df=28) |
| Intercept | 14 | 3.1125 | 2.34 |
| Distance–X | 6 | 0.8778 | 6.36 |
a-1. Determine the regression equation. (Round your answers to 3 decimal places.)
a-2. Is there a direct or indirect relationship between the distance from the fire station and the amount of fire damage?
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.)
c-1. Determine and interpret the coefficient of determination. (Round your answer to 3 decimal places.)
c-2. Fill in the blank below. (Round your answer to one decimal place.)
d-1. Determine the
d-2. Choose the right option.
d-3. How did you determine the sign of the correlation coefficient?
e-1. 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.)
e-2. Compute the value of the test statistic. (Round your answer to 2 decimal places.)
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.
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