The linear model below explores a potential associationbetween property damage and wind speed based on observational datafrom 94 hurricanes that hit the United States between 1950 and2012. The variables are

Damage: property damage in millions of U.S. dollars(adjusted for inflation to 2014) for each hurricane

Landfall.Windspeed: Maximum sustained windspeed in milesper hour measured along U.S. coast for each hurricane

* Assume that the sample data satisfies all assumptionsfor linear regression.

Level of significance = 0.05.   

> summary(model)

Call:

lm(formula = Damage ~ Landfall.Windspeed)

Residuals:

   Min 1Q Median 3Q Max

-9294 -4782 -1996 -531 90478

Coefficients:

         Estimate Std. Error t value Pr(>|t|)

(Intercept) -10041.78 6064.29 -1.656 0.1012

Landfall.Windspeed 142.07 56.65 2.508 0.0139*

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Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’ 1

Residual standard error: 12280 on 92 degrees offreedom

Multiple R-squared: [ A ], Adjusted R-squared:0.05381

F-statistic: 6.289 on 1 and 92 DF, p-value:0.01391

(a) Write the equation for the linear model using thevariables Damages and Landfall Windspeed, taking the results of thet-tests into account.

(b) A hurricane is defined as a storm with wind speedsgreater than 74 miles per hour. Interpret the value of theintercept in connection to the real-life context of this model (twoor three sentences). Hint: Is the intercept truly meaningful, giventhe definition of a hurricane?

(c) The value of Pearson’s correlation coefficient forDamages and Landfall.Windspeed is 0.2529438. Calculate andinterpret the value of R2 , denoted [A] in the table, in relationto the predictor and response variables.

(d) The range of observed maximum wind speeds in thesample data is 75 – 190 miles per hour. Is it appropriate to usethe linear model to predict the cost of damage for a hurricane witha maximum wind speed of 150 miles per hour? Why or why not? If so,estimate the typical value of damages (specifyingunits).

(e) Would it be appropriate to use the linear model topredict the cost of damage for a hurricane with a maximum windspeed of 225 miles per hour? Why or why not? If so, estimate thetypical value of damages (specifying units).