An insurance company suspects that there is a positive linear relationship betwe

Question

An insurance company suspects that there is a positive linear relationship between the dollar amount of fire damage in residential fires, and the distance between the residence and the nearest fire station. Data were collected on a random sample of 17 residential fires and the results are given below. The amount of fire damage (in thousands of dollars) is denoted as cost, and the distance between the residence and the nearest fire station (in miles) is denoted as distance.

Using Excel, generate a 90% interval for the dollar amount of fire damage for a residence that is 5.7 miles from the nearest fire station. (You have to decide if the interval is a confidence interval or a prediction interval)

From: __________________ To: ________________

Cost Distance 26 1.5 27 2.6 28 3.7 37 3.8 38 4.3 47 4.5 48 4.9 50 5.8 52 6.5 57 6.8 59 7.5 68 7.6 70 8.4 83 8.5 84 9.3 96 9.4 98 9.9

Explanation / Answer

Here we will use the prediciton interval, hence the interval is (40.89,64.616)

Regression output confidence interval variables coefficients std. error    t (df=15) p-value 90% lower 90% upper Intercept 2.6496 4.3010 0.616 .5471 -4.8903 10.1895 y 8.7901 0.6468 13.590 7.76E-10 7.6562 9.9240 Predicted values for: x 90% Confidence Interval 90% Prediction Interval y Predicted lower upper lower upper Leverage 5.7 52.753 49.908 55.598 40.890 64.616 0.061

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