Suppose a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. A random sample of 15 fires in a large suburb is selected. The amount of damage (thousands of dollars) and the distance (miles) between the fire and the nearest fire station are recorded for each fire. The following simple linear regression model was used: Fire Damage_i = ?0 + ?1(Distance from Fire Station)_i + ?_i Coefficients Std. Error Intercept 10.2779 1.4203 Distance 4.9193 0.3927 a) The response variable is: __________________ b) The explanatory variable is: __________________ c) The least squares regression line is: Fire damage = 10.2779 + 4.9193 (Distance from fire station) d) Find the predicted fire damage when a residential home is located 6 miles from the fire station. e) Suppose the researchers test the hypotheses: H0: ? = 0 versus Ha: ? > 0 The value of the t statistic for this test is: _______ f) The P-value for the t statistic found in part (e) is: _______ g) Based on parts (e) & (f) state your conclusion regarding the significance of ?. h) Give the interpretation of ?1. i) Give the interpretation of ?0.
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. A researcher wishes to investigate the relationship amongst the distance between a house and the closest fire station in kilometers X (independent variable) and the damage that fire caused to them in thousand dollars as a dependent variable Y. A sample of houses from different parts of the city is randomly selected and the results are summarized in the ANOVA table below: Degrees of Freedom SS Regression 1 841.77 Residual 13 69.75 Total 14 911.52 Coefficients Standard Error t Stat p-value Intercept 10.28 1.42 7.24 0.006 X variable 4.92 0.39 12.53 0.001 a. What is the estimated regression equation that relates the fire damage (Y) to the distance from the fire station (X)? b. If a property is 5.8 kilometers away from the closest fire station what is the estimated damage in thousands of dollars? c. Is the regression relationship significant? Use the p-value approach and 1% level of significance. d. Compute the coefficient of determination between distance and the fire damage. Interpret the result in the context of the problem.
Adi S.
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. $$ \begin{array}{|lrrrr|} \hline \text { ANOVA table } & & & & & & \\ \text { Source } & & \text { SS } & \text { df } & \text { MS } & \text { F } \\ \text { Regression } & 1,864.5782 & 1 & 1,864.5782 & 38.83 \\ \text { Residual } & 1,344.4934 & 28 & 48.0176 & \\ \text { Total } & 3,209.0716 & 29 & & & \\ \text { Regression } & \text { output } & & & & \\ \text { Variables } & \text { Coefficients } & \text { Std. Error } t(\mathrm{df} & =28) \\ \text { Intercept } & 12.3601 & & 3.2915 & 3.755 \\ \text { Distance-X } & 4.7956 & & 0.7696 & 6.231 \\ \hline \end{array} $$ Answer the following questions. a. Write out the regression equation. 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 5 miles from the nearest fire station? c. Determine and interpret the coefficient of determination. d. Determine the correlation coefficient. Interpret its value. How did you determine the sign of the correlation coefficient? e. Conduct a test of hypothesis to determine if there is a significant relationship between the distance from the fire station and the amount of damage. Use the .01 significance level and a two-tailed test.
Supposed a fire insurance company wants to relate the amount of fire damage in major residential fires to the distance between the burning house and the nearest fire station. The study is to be conducted in a large suburb of a major city; a sample of 15 recent fires in this suburb is selected. The amount of damage (1 unit = $1,000) and the distance between the fire and the nearest fire station (1 unit = mile) are recorded for each fire. The simple linear model y = β0 + β1 x was fit to the data. Computer printouts for the analysis are given below. 1. Give the least squares prediction equation. 2. Interpret the estimated slope.
David N.
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