Suppose that 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 conducted in a suburb of a major metropolitan area. The data collected were the distance in miles between the nearest fire station, and the fire and the amount of damage to the house in dollars. You may assume that the closest fire in the data set was 2 miles away from the fire station and the farthest fire in the data set was 8 miles away from the fire station. Use the information in the printout below to complete the following: Correlation of DISTANCE and FIRE DAMAGE = 0.91 The regression equation is: FIR DAMAGE = 9560 + 5020(DISTANCE) (a) Use a sentence to interpret the correlation coefficient. (b) Use a sentence to interpret the slope of the least squares regression line. (c) Use the least squares regression line to predict the amount of fire damage of a home that is 7 miles away from the nearest fire station. Be sure to include the appropriate units in your answer. (d) Use the least squares regression line to predict the amount of fire damage of a home that is 12 miles away from the nearest fire station. Be sure to include the appropriate units in your answer.
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91. This indicates a strong positive linear association between the distance from the fire station and the amount of fire damage. Show more…
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An insurance company determines that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. A sample of 15 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded: x= the distance between the fire and the nearest fire station (in miles) y= cost of damage (in dollars) The distances between the fire and the nearest fire station ranged between 0.7 miles and 6.1 miles. 1) The correlation between cost and distance is 0.961. What is the critical value for testing if the correlation is significant at α=.05? Give the exact value from the critical value table. 2) The correlation between cost and distance is 0.961. Test if the correlation is significant at α=.05. 3) What is the regression equation for predicting cost of damage from the distance between the fire and the nearest fire station when the slope is 4919, and the y-intercept is 10278 ? 4) Predict the cost of damage for a house that is 0.5 miles from the nearest fire station. Type either a numerical value or not appropriate. 5) Predict the cost of damage for a house that is 2 miles from the nearest fire station. Type either a numerical value or not appropriate. 6) The correlation between cost and distance is 0.961. Describe the relationship between cost of damage and distance from the nearest fire station. Group of answer choices
Ameer S.
Suppose that a fire insurance company wants to relate the amount of fire damage (in thousands of dollars) in major residential fires to the distance (in miles) 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. Distance: 3.4 1.8 4.6 2.3 3.1 5.5 0.7 3 2.6 4.3 2.1 1.1 6.1 4.8 3.8 Damage: 26.2 17.8 31.3 23.1 27.5 36 14.1 22.3 19.6 31.3 24 17.3 43.2 36.4 26.1 (a) What is the value of the correlation coefficient between Damage and Distance? What does this number mean within the context of this data? (b) Give the slope of the least squares line. Interpret this value within the context of Distance and Damage. (c) Write down the regression or prediction equation for predicting Damage in terms of Distance. (d) What is the "residual" associated with the fire which was 1.8 miles from the nearest fire station? Explain what the value of the residual means in the context of the problem. (e) Find a 95% confidence interval for the mean fire damage (in $) associated with fire which was 1.8 miles from the nearest fire station? (f) Find a 95% prediction interval for the fire damage (in $) associated with fire which was 1.8 miles from the nearest fire station? (g) Obtain a 90% confidence interval for the population slope? (h) Give an interpretation of what the 90% confidence interval for the population slope means in the context of the problem? (i) An Insurance broker had claimed that the cost of damage increases by US$4,500 on average, for every mile away from the fire station. Based on part (g) above, what can you say about the broker's claim? (j) Use the 5 or 6 step process to test the hypothesis that there exists a true linear relationship between damage and distance. (k) Identify the type of problem (choices are: One Quant Var (includes paired data), One Categ Var, Two Categ Vars, Two Indep Samples/Pops, More than Two Indep Samples/Pops, Bivariate Samples/Pops or Multivariate Samples/Pops)
Umar Sohail Q.
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.
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